V poslední třetině 10. století se na křesťanských latinských školách začíná opětovně užívat matem... more V poslední třetině 10. století se na křesťanských latinských školách začíná opětovně užívat matematická počtářská pomůcka zvaná Pýthagorova tabule (mensa Pythagorica) nebo také geometrická deska (mensa geometricalis) čili abakus. Za čelní protagonisty užívání nové podoby tohoto nástroje lze označit Gerberta z Remeše (zvaného rovněž z Aurillacu, z Bobbia či z Ravenny, papež Silvestr II.) nebo jeho následovníka Bernelina mladšího z Paříže. V této knize jsou bilingvně latinsko-česky publikovány jejich texty o způsobech, jak na abaku počítat – Gerbertova Pravidla počítání na abaku (Regulae de numerorum abaci rationibus) a Bernelinova Kniha o abaku (Liber abaci). Těmto spisům předchází úvodní studie seznamující s tradicí abacistického počtářství na latinském křesťanském Západě a knihu završují přílohy, v nichž jsou graficky zachyceny výpočty na abacistické desce, jak je ve svých dílech oba středověcí autoři popsali.
Während die Urkundenlehre zu einem Klassiker der mediävistischen Forschung zählt, führt die mitte... more Während die Urkundenlehre zu einem Klassiker der mediävistischen Forschung zählt, führt die mittelalterliche Briefstillehre ein Schattendasein, obwohl vom 11. bis 15 Jahrhundert Hunderte von Briefstillehren (artes dictandi) in über 10.000 Handschriften überliefert sind. Ein umfassendes Werk oder Handbuch zu dieser wirkmächtigen Gattung fehlt bis heute. Dabei lassen sich diese Texte über das Verfassen von öffentlichen Schreiben als Norm für die ‚richtige’ Kommunikation lesen. Schließlich wirkten die in ihnen etablierten Vorstellungen affirmativ und normativ in die Gesellschaft zurück. Das Potential der Texte für historische und philologische Fragestellungen wurde in den letzten Jahren immer stärker artikuliert. Vor diesem Hintergrund wird jetzt erstmals eine auf der Quellenkenntnis eines Autorenkollektivs basierende Entwicklungsgeschichte der mittelalterlichen ars dictaminis vorgelegt.
Chancery notes on papal letters in time 1378-1417 based on papal letters survived in Moravian arc... more Chancery notes on papal letters in time 1378-1417 based on papal letters survived in Moravian archives
This work is based on the study and comparison of originals of the papal documents from the period between the years 1378-1417, which are now kept in the archives in Moravia and Czech Silesia. Altogether, we have collected and processed 59 documents of the popes of the Roman and the Pisan obedience from the period of the schism and two documents of the Council of Constance. Analysis of the chancery notes on these documents and their comparison with the data published by the project ?Censimento? showed, or rather confirmed, some phenomena, changes and trends in issuing papal documents at the time of the schism. The development in the curial offices of the Avignon popes could not be observed due to the understandable absence of these documents in the monitored archives.
Pope Silvester II. (pont. 999–1003) born Gerbert of Reims or Aurillac, Bobbio or of Ravenna, belo... more Pope Silvester II. (pont. 999–1003) born Gerbert of Reims or Aurillac, Bobbio or of Ravenna, belongs among the most famous personalities of the Latin speaking Christian world around the period of the first millennium. The life of this important diplomat is closely bound to Ottonian house as well as to a fight for the French crown between Carolingian and Capet dynasties. Gerbert became during his life an (non-legitimate) archbishop of Reims, abbot of the St. Columbanus monastery in Bobbio, archbishop of Ravenna and finally the pope. According to medieval so-called Gerbert’s legend, Gerbert achieved all these positions with help of devil and thanks to the devil’s intervention he also became one of the most noted scholars and teachers of his time. His influential pupils (above all kings and emperors) then did not hesitate to appoint him with various church offices. Gerbert of Reims holds a firm position in history of philosophy and scientific thinking. Measured by today’s categories he can be noted as an important astronomer, logician, rhetorician, philosopher or mathematician who was also active in music theory and praxis, geometry as well as in area of practical and theoretical arithmetic. The last mentioned activity is subject of this book bringing the Latin original and Czech translation of seven Gerbert’s letters dedicated to mathematics. First five of them were addressed to Gerbert’s friend, co-operator and perhaps pupil Constantine of Fleury. All letters to Constantine were written by the end of the 70-ties or at the beginning of the 80-ties of the 10th century, therefore during the time when Gerbert worked as teacher in Reims. Letter 1 is reaction to the period debate on conversion of three-membered numerical sequences arranged according to a certain ratio in the three same sums. Gerbert, following Boethius’s Introduction to arithmetic, deals with a conversion of superparticular numbers arranged in ratio 5:4 to a parity, i.e. ratio 1:1 and vigorously delimits the non-systematic method that was probably commonly used, however without respecting the nature of numbers, metaphysical hierarchy of relationships between the numerical ratios and ignoring the Boethius’s rules of conversions. Numerous and clear rejection of alternative approach of the ratios conversion is not even reduced by mathematical final correctness of the unrecognized method. Letters 2 and 3 represent Gerbert’s commentaries on various text passages of Boethius’s Introduction to music. Boethius’s work is always quoted at first then Gerbert explains the arithmetic base of the quoted postulate. In Letter 2 Gerbert targets multiplication of ratios and classification of resulting products according to relative nature of numbers. Letter 3 describes and by using specific example clarifies a process of subtraction of smaller superparticular ratio from immediately subsequently bigger superparticular ratio. The resulting difference was found smaller then half of the subtracted ratio (subtrahend) as the double quantity of the result is a semitone smaller then subtracted ratio. While the first three Gerbert’s letters are dedicated to theoretical arithmetic, Letters 4 and 5 represent an accompanying text of an abacist tract. Their subject is introduction to practical arithmetic, i.e. computing. Both abacist letters have very similar structures: Gerbert praises Constantine for his interest in study; and more he calls him consolation of his struggle and reason for writing the abacist treatises. Then Gerbert delimits himself towards other period scholars who only mention the abacus computations, however Gerbert criticises them for their disinterest in scientific texts of older authorities as well as for inability to understand neither the basic principles of abacus numeration nor methods of arithmetic computations. Another two Gerbert’s mathematic letters were written in later period of Gerbert’s life (Letter 6 in year 988, Letter 7 probably in year 999). Both are part of a correspondence between Gerbert and Remigius of Trier (Letter 6) and Adelbold of Utrecht (Letter 7). First of the two letters deals in its mathematic part with divisible numbers, i.e. with way of measuring one number by another one. This topic is also linked to abacus numeration as well as to disintegration of numbers according to superparticular ratios. Letter 7 in general manner as well as with help of the specific examples explains different method of expressing the surface area of equilateral triangle using geometric and mathematic skill. Individual letters are accompanied by commentaries closely introducing mainly the historical context of the individual problem and mathematic method presented in Gerbert’s letters. The book opens an introductory study in order to ease orientation in the topics targeted by Gerbert’s mathematic letters as well as to closely present Boethius’s Introduction to arithmetic, the theoretical base of arithmetic knowledge initial for Gerbert’s texts (especially a character of number as such, character of numbers in relation to other numbers, i.e. above all number measuring or numeral sequences and ratios, further long also figural numbers and their discovering and depicting). Early medieval abacus computing tradition is also briefly presented including the design and structure of this unique mathematic device. The introduction to theoretical and practical arithmetic is preceded by condensed description of Gerbert’s personality. The author of the letters is mainly presented as an important scholar of his period who was also very active in field of diplomacy. The book doesn’t miss out so called Gerbert’s legend reflecting already during the medieval period the personality of the great intellectual and mathematician.
1. vyd. Kniha o první filosofii neboli božské vědě : traktát první = Liber De philosophia prima s... more 1. vyd. Kniha o první filosofii neboli božské vědě : traktát první = Liber De philosophia prima sive scientia divina : tractatus primus / Avicenna -- Epitomé k Aristotelově Metafyzice : traktát první = Epitome in librum Metaphisicae Aristotelis : tractatus primus / Averroes z Cordóby
Monografie je zaměřena na podobu zakladnich edicnich řad v kontextu potřeb soucasne a budouci his... more Monografie je zaměřena na podobu zakladnich edicnich řad v kontextu potřeb soucasne a budouci historicke vědy; okrajově je přihlednuto i k jiným pramenům diplomaticke povahy. Exploze výpocetni techniky a medialnich technologii v poslednim desetileti znamenaji zlom, který musi být zohledněn při formulaci edicni techniky prakticky vsech edicnich řad, na kterých se v soucasnosti pracuje.
The article deals with the sermon collection entitled Sermones de principalibus festis, by Peter ... more The article deals with the sermon collection entitled Sermones de principalibus festis, by Peter of Zittau (d. 1339). The collection has survived in a single manuscriptcodex Ms 434 at Leipzig University Library. Drawing on the results of paleographic, codicological and textual analysis of codex Ms 434, the authors explore what the manuscript record of the sermons reveals about the genesis of the texts and Peter of Zittau's working methods. Particular attention is paid to the numerous corrections which were added to the text of the sermons (as copied into the codex by a scribe) by a different contemporary hand. Based on an analysis of the nature of these corrections and a comparison of the handwriting with that of Peter of Zittau (as known from the autograph of the second book of his Chronica Aulae regiae), the paper tests the hypothesis that the author of the corrections in manuscript Ms 434 was Peter of Zittau himself.
The study is dedicated to development of the Olomouc bishop’s seals in period between 1351 and 14... more The study is dedicated to development of the Olomouc bishop’s seals in period between 1351 and 1457 with emphasis on their iconography. From the artistic point of view the analysed seals from above stated period represent the highest quality. In the same period we can notice significant transformation of typology of used matrixes. The study shows that those changes in some cases reflect the period mentality. The authors of the article also mention reasons that could motivate the individual bishops to choose the particular iconographic type. In that sense the authors further on analyse the basic iconographic motifs. The catalogue of the Episcopal seals represents the core of the study as well as the description of the official Coat of arms evolution till the end of the 15th century.
ABSTRACT 1. vyd. Kniha o první filosofii neboli božské vědě : traktát první = Liber De philosophi... more ABSTRACT 1. vyd. Kniha o první filosofii neboli božské vědě : traktát první = Liber De philosophia prima sive scientia divina : tractatus primus / Avicenna -- Epitomé k Aristotelově Metafyzice : traktát první = Epitome in librum Metaphisicae Aristotelis : tractatus primus / Averroes z Cordóby
Pope Silvester II. (pont. 999–1003) born Gerbert of Reims or Aurillac, Bobbio or of Ravenna, belo... more Pope Silvester II. (pont. 999–1003) born Gerbert of Reims or Aurillac, Bobbio or of Ravenna, belongs among the most famous personalities of the Latin speaking Christian world around the period of the first millennium. The life of this important diplomat is closely bound to Ottonian house as well as to a fight for the French crown between Carolingian and Capet dynasties. Gerbert became during his life an (non-legitimate) archbishop of Reims, abbot of the St. Columbanus monastery in Bobbio, archbishop of Ravenna and finally the pope. According to medieval so-called Gerbert’s legend, Gerbert achieved all these positions with help of devil and thanks to the devil’s intervention he also became one of the most noted scholars and teachers of his time. His influential pupils (above all kings and emperors) then did not hesitate to appoint him with various church offices. Gerbert of Reims holds a firm position in history of philosophy and scientific thinking. Measured by today’s categories he can be noted as an important astronomer, logician, rhetorician, philosopher or mathematician who was also active in music theory and praxis, geometry as well as in area of practical and theoretical arithmetic. The last mentioned activity is subject of this book bringing the Latin original and Czech translation of seven Gerbert’s letters dedicated to mathematics. First five of them were addressed to Gerbert’s friend, co-operator and perhaps pupil Constantine of Fleury. All letters to Constantine were written by the end of the 70-ties or at the beginning of the 80-ties of the 10th century, therefore during the time when Gerbert worked as teacher in Reims. Letter 1 is reaction to the period debate on conversion of three-membered numerical sequences arranged according to a certain ratio in the three same sums. Gerbert, following Boethius’s Introduction to arithmetic, deals with a conversion of superparticular numbers arranged in ratio 5:4 to a parity, i.e. ratio 1:1 and vigorously delimits the non-systematic method that was probably commonly used, however without respecting the nature of numbers, metaphysical hierarchy of relationships between the numerical ratios and ignoring the Boethius’s rules of conversions. Numerous and clear rejection of alternative approach of the ratios conversion is not even reduced by mathematical final correctness of the unrecognized method. Letters 2 and 3 represent Gerbert’s commentaries on various text passages of Boethius’s Introduction to music. Boethius’s work is always quoted at first then Gerbert explains the arithmetic base of the quoted postulate. In Letter 2 Gerbert targets multiplication of ratios and classification of resulting products according to relative nature of numbers. Letter 3 describes and by using specific example clarifies a process of subtraction of smaller superparticular ratio from immediately subsequently bigger superparticular ratio. The resulting difference was found smaller then half of the subtracted ratio (subtrahend) as the double quantity of the result is a semitone smaller then subtracted ratio. While the first three Gerbert’s letters are dedicated to theoretical arithmetic, Letters 4 and 5 represent an accompanying text of an abacist tract. Their subject is introduction to practical arithmetic, i.e. computing. Both abacist letters have very similar structures: Gerbert praises Constantine for his interest in study; and more he calls him consolation of his struggle and reason for writing the abacist treatises. Then Gerbert delimits himself towards other period scholars who only mention the abacus computations, however Gerbert criticises them for their disinterest in scientific texts of older authorities as well as for inability to understand neither the basic principles of abacus numeration nor methods of arithmetic computations. Another two Gerbert’s mathematic letters were written in later period of Gerbert’s life (Letter 6 in year 988, Letter 7 probably in year 999). Both are part of a correspondence between Gerbert and Remigius of Trier (Letter 6) and Adelbold of Utrecht (Letter 7). First of the two letters deals in its mathematic part with divisible numbers, i.e. with way of measuring one number by another one. This topic is also linked to abacus numeration as well as to disintegration of numbers according to superparticular ratios. Letter 7 in general manner as well as with help of the specific examples explains different method of expressing the surface area of equilateral triangle using geometric and mathematic skill. Individual letters are accompanied by commentaries closely introducing mainly the historical context of the individual problem and mathematic method presented in Gerbert’s letters. The book opens an introductory study in order to ease orientation in the topics targeted by Gerbert’s mathematic letters as well as to closely present Boethius’s Introduction to arithmetic, the theoretical base of arithmetic knowledge initial for Gerbert’s texts…
In: Časopis Matice moravské 133, 2014, 2, s. 359-380
Dating two medieval papal documents from th... more In: Časopis Matice moravské 133, 2014, 2, s. 359-380
Dating two medieval papal documents from the funds of the Moraviam Land Archive in Brno. A contribution to the history the Augustinian Eremites and the Cistercian Monastery in Velehrad.
The contribution focuses on two papal letters addressed to two different monastic institutions, whose dating in archive inventaries, as preserved in the editions, remains spurious. The documents are not connected and their thematic bond lies in the institu- tional position of their publisher and in the questions related to their uncertain dating. The study aims to prove, based on the diplomatic-paleographic analysis and material study, that the traditionally acepted dates need to be adjusted and both documents must be placed within their probable chronological context.
V poslední třetině 10. století se na křesťanských latinských školách začíná opětovně užívat matem... more V poslední třetině 10. století se na křesťanských latinských školách začíná opětovně užívat matematická počtářská pomůcka zvaná Pýthagorova tabule (mensa Pythagorica) nebo také geometrická deska (mensa geometricalis) čili abakus. Za čelní protagonisty užívání nové podoby tohoto nástroje lze označit Gerberta z Remeše (zvaného rovněž z Aurillacu, z Bobbia či z Ravenny, papež Silvestr II.) nebo jeho následovníka Bernelina mladšího z Paříže. V této knize jsou bilingvně latinsko-česky publikovány jejich texty o způsobech, jak na abaku počítat – Gerbertova Pravidla počítání na abaku (Regulae de numerorum abaci rationibus) a Bernelinova Kniha o abaku (Liber abaci). Těmto spisům předchází úvodní studie seznamující s tradicí abacistického počtářství na latinském křesťanském Západě a knihu završují přílohy, v nichž jsou graficky zachyceny výpočty na abacistické desce, jak je ve svých dílech oba středověcí autoři popsali.
Während die Urkundenlehre zu einem Klassiker der mediävistischen Forschung zählt, führt die mitte... more Während die Urkundenlehre zu einem Klassiker der mediävistischen Forschung zählt, führt die mittelalterliche Briefstillehre ein Schattendasein, obwohl vom 11. bis 15 Jahrhundert Hunderte von Briefstillehren (artes dictandi) in über 10.000 Handschriften überliefert sind. Ein umfassendes Werk oder Handbuch zu dieser wirkmächtigen Gattung fehlt bis heute. Dabei lassen sich diese Texte über das Verfassen von öffentlichen Schreiben als Norm für die ‚richtige’ Kommunikation lesen. Schließlich wirkten die in ihnen etablierten Vorstellungen affirmativ und normativ in die Gesellschaft zurück. Das Potential der Texte für historische und philologische Fragestellungen wurde in den letzten Jahren immer stärker artikuliert. Vor diesem Hintergrund wird jetzt erstmals eine auf der Quellenkenntnis eines Autorenkollektivs basierende Entwicklungsgeschichte der mittelalterlichen ars dictaminis vorgelegt.
Chancery notes on papal letters in time 1378-1417 based on papal letters survived in Moravian arc... more Chancery notes on papal letters in time 1378-1417 based on papal letters survived in Moravian archives
This work is based on the study and comparison of originals of the papal documents from the period between the years 1378-1417, which are now kept in the archives in Moravia and Czech Silesia. Altogether, we have collected and processed 59 documents of the popes of the Roman and the Pisan obedience from the period of the schism and two documents of the Council of Constance. Analysis of the chancery notes on these documents and their comparison with the data published by the project ?Censimento? showed, or rather confirmed, some phenomena, changes and trends in issuing papal documents at the time of the schism. The development in the curial offices of the Avignon popes could not be observed due to the understandable absence of these documents in the monitored archives.
Pope Silvester II. (pont. 999–1003) born Gerbert of Reims or Aurillac, Bobbio or of Ravenna, belo... more Pope Silvester II. (pont. 999–1003) born Gerbert of Reims or Aurillac, Bobbio or of Ravenna, belongs among the most famous personalities of the Latin speaking Christian world around the period of the first millennium. The life of this important diplomat is closely bound to Ottonian house as well as to a fight for the French crown between Carolingian and Capet dynasties. Gerbert became during his life an (non-legitimate) archbishop of Reims, abbot of the St. Columbanus monastery in Bobbio, archbishop of Ravenna and finally the pope. According to medieval so-called Gerbert’s legend, Gerbert achieved all these positions with help of devil and thanks to the devil’s intervention he also became one of the most noted scholars and teachers of his time. His influential pupils (above all kings and emperors) then did not hesitate to appoint him with various church offices. Gerbert of Reims holds a firm position in history of philosophy and scientific thinking. Measured by today’s categories he can be noted as an important astronomer, logician, rhetorician, philosopher or mathematician who was also active in music theory and praxis, geometry as well as in area of practical and theoretical arithmetic. The last mentioned activity is subject of this book bringing the Latin original and Czech translation of seven Gerbert’s letters dedicated to mathematics. First five of them were addressed to Gerbert’s friend, co-operator and perhaps pupil Constantine of Fleury. All letters to Constantine were written by the end of the 70-ties or at the beginning of the 80-ties of the 10th century, therefore during the time when Gerbert worked as teacher in Reims. Letter 1 is reaction to the period debate on conversion of three-membered numerical sequences arranged according to a certain ratio in the three same sums. Gerbert, following Boethius’s Introduction to arithmetic, deals with a conversion of superparticular numbers arranged in ratio 5:4 to a parity, i.e. ratio 1:1 and vigorously delimits the non-systematic method that was probably commonly used, however without respecting the nature of numbers, metaphysical hierarchy of relationships between the numerical ratios and ignoring the Boethius’s rules of conversions. Numerous and clear rejection of alternative approach of the ratios conversion is not even reduced by mathematical final correctness of the unrecognized method. Letters 2 and 3 represent Gerbert’s commentaries on various text passages of Boethius’s Introduction to music. Boethius’s work is always quoted at first then Gerbert explains the arithmetic base of the quoted postulate. In Letter 2 Gerbert targets multiplication of ratios and classification of resulting products according to relative nature of numbers. Letter 3 describes and by using specific example clarifies a process of subtraction of smaller superparticular ratio from immediately subsequently bigger superparticular ratio. The resulting difference was found smaller then half of the subtracted ratio (subtrahend) as the double quantity of the result is a semitone smaller then subtracted ratio. While the first three Gerbert’s letters are dedicated to theoretical arithmetic, Letters 4 and 5 represent an accompanying text of an abacist tract. Their subject is introduction to practical arithmetic, i.e. computing. Both abacist letters have very similar structures: Gerbert praises Constantine for his interest in study; and more he calls him consolation of his struggle and reason for writing the abacist treatises. Then Gerbert delimits himself towards other period scholars who only mention the abacus computations, however Gerbert criticises them for their disinterest in scientific texts of older authorities as well as for inability to understand neither the basic principles of abacus numeration nor methods of arithmetic computations. Another two Gerbert’s mathematic letters were written in later period of Gerbert’s life (Letter 6 in year 988, Letter 7 probably in year 999). Both are part of a correspondence between Gerbert and Remigius of Trier (Letter 6) and Adelbold of Utrecht (Letter 7). First of the two letters deals in its mathematic part with divisible numbers, i.e. with way of measuring one number by another one. This topic is also linked to abacus numeration as well as to disintegration of numbers according to superparticular ratios. Letter 7 in general manner as well as with help of the specific examples explains different method of expressing the surface area of equilateral triangle using geometric and mathematic skill. Individual letters are accompanied by commentaries closely introducing mainly the historical context of the individual problem and mathematic method presented in Gerbert’s letters. The book opens an introductory study in order to ease orientation in the topics targeted by Gerbert’s mathematic letters as well as to closely present Boethius’s Introduction to arithmetic, the theoretical base of arithmetic knowledge initial for Gerbert’s texts (especially a character of number as such, character of numbers in relation to other numbers, i.e. above all number measuring or numeral sequences and ratios, further long also figural numbers and their discovering and depicting). Early medieval abacus computing tradition is also briefly presented including the design and structure of this unique mathematic device. The introduction to theoretical and practical arithmetic is preceded by condensed description of Gerbert’s personality. The author of the letters is mainly presented as an important scholar of his period who was also very active in field of diplomacy. The book doesn’t miss out so called Gerbert’s legend reflecting already during the medieval period the personality of the great intellectual and mathematician.
1. vyd. Kniha o první filosofii neboli božské vědě : traktát první = Liber De philosophia prima s... more 1. vyd. Kniha o první filosofii neboli božské vědě : traktát první = Liber De philosophia prima sive scientia divina : tractatus primus / Avicenna -- Epitomé k Aristotelově Metafyzice : traktát první = Epitome in librum Metaphisicae Aristotelis : tractatus primus / Averroes z Cordóby
Monografie je zaměřena na podobu zakladnich edicnich řad v kontextu potřeb soucasne a budouci his... more Monografie je zaměřena na podobu zakladnich edicnich řad v kontextu potřeb soucasne a budouci historicke vědy; okrajově je přihlednuto i k jiným pramenům diplomaticke povahy. Exploze výpocetni techniky a medialnich technologii v poslednim desetileti znamenaji zlom, který musi být zohledněn při formulaci edicni techniky prakticky vsech edicnich řad, na kterých se v soucasnosti pracuje.
The article deals with the sermon collection entitled Sermones de principalibus festis, by Peter ... more The article deals with the sermon collection entitled Sermones de principalibus festis, by Peter of Zittau (d. 1339). The collection has survived in a single manuscriptcodex Ms 434 at Leipzig University Library. Drawing on the results of paleographic, codicological and textual analysis of codex Ms 434, the authors explore what the manuscript record of the sermons reveals about the genesis of the texts and Peter of Zittau's working methods. Particular attention is paid to the numerous corrections which were added to the text of the sermons (as copied into the codex by a scribe) by a different contemporary hand. Based on an analysis of the nature of these corrections and a comparison of the handwriting with that of Peter of Zittau (as known from the autograph of the second book of his Chronica Aulae regiae), the paper tests the hypothesis that the author of the corrections in manuscript Ms 434 was Peter of Zittau himself.
The study is dedicated to development of the Olomouc bishop’s seals in period between 1351 and 14... more The study is dedicated to development of the Olomouc bishop’s seals in period between 1351 and 1457 with emphasis on their iconography. From the artistic point of view the analysed seals from above stated period represent the highest quality. In the same period we can notice significant transformation of typology of used matrixes. The study shows that those changes in some cases reflect the period mentality. The authors of the article also mention reasons that could motivate the individual bishops to choose the particular iconographic type. In that sense the authors further on analyse the basic iconographic motifs. The catalogue of the Episcopal seals represents the core of the study as well as the description of the official Coat of arms evolution till the end of the 15th century.
ABSTRACT 1. vyd. Kniha o první filosofii neboli božské vědě : traktát první = Liber De philosophi... more ABSTRACT 1. vyd. Kniha o první filosofii neboli božské vědě : traktát první = Liber De philosophia prima sive scientia divina : tractatus primus / Avicenna -- Epitomé k Aristotelově Metafyzice : traktát první = Epitome in librum Metaphisicae Aristotelis : tractatus primus / Averroes z Cordóby
Pope Silvester II. (pont. 999–1003) born Gerbert of Reims or Aurillac, Bobbio or of Ravenna, belo... more Pope Silvester II. (pont. 999–1003) born Gerbert of Reims or Aurillac, Bobbio or of Ravenna, belongs among the most famous personalities of the Latin speaking Christian world around the period of the first millennium. The life of this important diplomat is closely bound to Ottonian house as well as to a fight for the French crown between Carolingian and Capet dynasties. Gerbert became during his life an (non-legitimate) archbishop of Reims, abbot of the St. Columbanus monastery in Bobbio, archbishop of Ravenna and finally the pope. According to medieval so-called Gerbert’s legend, Gerbert achieved all these positions with help of devil and thanks to the devil’s intervention he also became one of the most noted scholars and teachers of his time. His influential pupils (above all kings and emperors) then did not hesitate to appoint him with various church offices. Gerbert of Reims holds a firm position in history of philosophy and scientific thinking. Measured by today’s categories he can be noted as an important astronomer, logician, rhetorician, philosopher or mathematician who was also active in music theory and praxis, geometry as well as in area of practical and theoretical arithmetic. The last mentioned activity is subject of this book bringing the Latin original and Czech translation of seven Gerbert’s letters dedicated to mathematics. First five of them were addressed to Gerbert’s friend, co-operator and perhaps pupil Constantine of Fleury. All letters to Constantine were written by the end of the 70-ties or at the beginning of the 80-ties of the 10th century, therefore during the time when Gerbert worked as teacher in Reims. Letter 1 is reaction to the period debate on conversion of three-membered numerical sequences arranged according to a certain ratio in the three same sums. Gerbert, following Boethius’s Introduction to arithmetic, deals with a conversion of superparticular numbers arranged in ratio 5:4 to a parity, i.e. ratio 1:1 and vigorously delimits the non-systematic method that was probably commonly used, however without respecting the nature of numbers, metaphysical hierarchy of relationships between the numerical ratios and ignoring the Boethius’s rules of conversions. Numerous and clear rejection of alternative approach of the ratios conversion is not even reduced by mathematical final correctness of the unrecognized method. Letters 2 and 3 represent Gerbert’s commentaries on various text passages of Boethius’s Introduction to music. Boethius’s work is always quoted at first then Gerbert explains the arithmetic base of the quoted postulate. In Letter 2 Gerbert targets multiplication of ratios and classification of resulting products according to relative nature of numbers. Letter 3 describes and by using specific example clarifies a process of subtraction of smaller superparticular ratio from immediately subsequently bigger superparticular ratio. The resulting difference was found smaller then half of the subtracted ratio (subtrahend) as the double quantity of the result is a semitone smaller then subtracted ratio. While the first three Gerbert’s letters are dedicated to theoretical arithmetic, Letters 4 and 5 represent an accompanying text of an abacist tract. Their subject is introduction to practical arithmetic, i.e. computing. Both abacist letters have very similar structures: Gerbert praises Constantine for his interest in study; and more he calls him consolation of his struggle and reason for writing the abacist treatises. Then Gerbert delimits himself towards other period scholars who only mention the abacus computations, however Gerbert criticises them for their disinterest in scientific texts of older authorities as well as for inability to understand neither the basic principles of abacus numeration nor methods of arithmetic computations. Another two Gerbert’s mathematic letters were written in later period of Gerbert’s life (Letter 6 in year 988, Letter 7 probably in year 999). Both are part of a correspondence between Gerbert and Remigius of Trier (Letter 6) and Adelbold of Utrecht (Letter 7). First of the two letters deals in its mathematic part with divisible numbers, i.e. with way of measuring one number by another one. This topic is also linked to abacus numeration as well as to disintegration of numbers according to superparticular ratios. Letter 7 in general manner as well as with help of the specific examples explains different method of expressing the surface area of equilateral triangle using geometric and mathematic skill. Individual letters are accompanied by commentaries closely introducing mainly the historical context of the individual problem and mathematic method presented in Gerbert’s letters. The book opens an introductory study in order to ease orientation in the topics targeted by Gerbert’s mathematic letters as well as to closely present Boethius’s Introduction to arithmetic, the theoretical base of arithmetic knowledge initial for Gerbert’s texts…
In: Časopis Matice moravské 133, 2014, 2, s. 359-380
Dating two medieval papal documents from th... more In: Časopis Matice moravské 133, 2014, 2, s. 359-380
Dating two medieval papal documents from the funds of the Moraviam Land Archive in Brno. A contribution to the history the Augustinian Eremites and the Cistercian Monastery in Velehrad.
The contribution focuses on two papal letters addressed to two different monastic institutions, whose dating in archive inventaries, as preserved in the editions, remains spurious. The documents are not connected and their thematic bond lies in the institu- tional position of their publisher and in the questions related to their uncertain dating. The study aims to prove, based on the diplomatic-paleographic analysis and material study, that the traditionally acepted dates need to be adjusted and both documents must be placed within their probable chronological context.
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Books by Richard Psik
This work is based on the study and comparison of originals of the papal documents from the period between the years 1378-1417, which are now kept in the archives in Moravia and Czech Silesia. Altogether, we have collected and processed 59 documents of the popes of the Roman and the Pisan obedience from the period of the schism and two documents of the Council of Constance. Analysis of the chancery notes on these documents and their comparison with the data published by the project ?Censimento? showed, or rather confirmed, some phenomena, changes and trends in issuing papal documents at the time of the schism. The development in the curial offices of the Avignon popes could not be observed due to the understandable absence of these documents in the monitored archives.
Gerbert of Reims holds a firm position in history of philosophy and scientific thinking. Measured by today’s categories he can be noted as an important astronomer, logician, rhetorician, philosopher or mathematician who was also active in music theory and praxis, geometry as well as in area of practical and theoretical arithmetic. The last mentioned activity is subject of this book bringing the Latin original and Czech translation of seven Gerbert’s letters dedicated to mathematics.
First five of them were addressed to Gerbert’s friend, co-operator and perhaps pupil Constantine of Fleury. All letters to Constantine were written by the end of the 70-ties or at the beginning of the 80-ties of the 10th century, therefore during the time when Gerbert worked as teacher in Reims. Letter 1 is reaction to the period debate on conversion of three-membered numerical sequences arranged according to a certain ratio in the three same sums. Gerbert, following Boethius’s Introduction to arithmetic, deals with a conversion of superparticular numbers arranged in ratio 5:4 to a parity, i.e. ratio 1:1 and vigorously delimits the non-systematic method that was probably commonly used, however without respecting the nature of numbers, metaphysical hierarchy of relationships between the numerical ratios and ignoring the Boethius’s rules of conversions. Numerous and clear rejection of alternative approach of the ratios conversion is not even reduced by mathematical final correctness of the unrecognized method.
Letters 2 and 3 represent Gerbert’s commentaries on various text passages of Boethius’s Introduction to music. Boethius’s work is always quoted at first then Gerbert explains the arithmetic base of the quoted postulate. In Letter 2 Gerbert targets multiplication of ratios and classification of resulting products according to relative nature of numbers. Letter 3 describes and by using specific example clarifies a process of subtraction of smaller superparticular ratio from immediately subsequently bigger superparticular ratio. The resulting difference was found smaller then half of the subtracted ratio (subtrahend) as the double quantity of the result is a semitone smaller then subtracted ratio.
While the first three Gerbert’s letters are dedicated to theoretical arithmetic, Letters 4 and 5 represent an accompanying text of an abacist tract. Their subject is introduction to practical arithmetic, i.e. computing. Both abacist letters have very similar structures: Gerbert praises Constantine for his interest in study; and more he calls him consolation of his struggle and reason for writing the abacist treatises. Then Gerbert delimits himself towards other period scholars who only mention the abacus computations, however Gerbert criticises them for their disinterest in scientific texts of older authorities as well as for inability to understand neither the basic principles of abacus numeration nor methods of arithmetic computations.
Another two Gerbert’s mathematic letters were written in later period of Gerbert’s life (Letter 6 in year 988, Letter 7 probably in year 999). Both are part of a correspondence between Gerbert and Remigius of Trier (Letter 6) and Adelbold of Utrecht (Letter 7). First of the two letters deals in its mathematic part with divisible numbers, i.e. with way of measuring one number by another one. This topic is also linked to abacus numeration as well as to disintegration of numbers according to superparticular ratios. Letter 7 in general manner as well as with help of the specific examples explains different method of expressing the surface area of equilateral triangle using geometric and mathematic skill.
Individual letters are accompanied by commentaries closely introducing mainly the historical context of the individual problem and mathematic method presented in Gerbert’s letters.
The book opens an introductory study in order to ease orientation in the topics targeted by Gerbert’s mathematic letters as well as to closely present Boethius’s Introduction to arithmetic, the theoretical base of arithmetic knowledge initial for Gerbert’s texts (especially a character of number as such, character of numbers in relation to other numbers, i.e. above all number measuring or numeral sequences and ratios, further long also figural numbers and their discovering and depicting). Early medieval abacus computing tradition is also briefly presented including the design and structure of this unique mathematic device.
The introduction to theoretical and practical arithmetic is preceded by condensed description of Gerbert’s personality. The author of the letters is mainly presented as an important scholar of his period who was also very active in field of diplomacy. The book doesn’t miss out so called Gerbert’s legend reflecting already during the medieval period the personality of the great intellectual and mathematician.
Papers by Richard Psik
Dating two medieval papal documents from the funds of the Moraviam Land Archive in Brno. A contribution to the history the Augustinian Eremites and the Cistercian Monastery in Velehrad.
The contribution focuses on two papal letters addressed to two different monastic institutions, whose dating in archive inventaries, as preserved in the editions, remains spurious. The documents are not connected and their thematic bond lies in the institu- tional position of their publisher and in the questions related to their uncertain dating. The study aims to prove, based on the diplomatic-paleographic analysis and material study, that the traditionally acepted dates need to be adjusted and both documents must be placed within their probable chronological context.
This work is based on the study and comparison of originals of the papal documents from the period between the years 1378-1417, which are now kept in the archives in Moravia and Czech Silesia. Altogether, we have collected and processed 59 documents of the popes of the Roman and the Pisan obedience from the period of the schism and two documents of the Council of Constance. Analysis of the chancery notes on these documents and their comparison with the data published by the project ?Censimento? showed, or rather confirmed, some phenomena, changes and trends in issuing papal documents at the time of the schism. The development in the curial offices of the Avignon popes could not be observed due to the understandable absence of these documents in the monitored archives.
Gerbert of Reims holds a firm position in history of philosophy and scientific thinking. Measured by today’s categories he can be noted as an important astronomer, logician, rhetorician, philosopher or mathematician who was also active in music theory and praxis, geometry as well as in area of practical and theoretical arithmetic. The last mentioned activity is subject of this book bringing the Latin original and Czech translation of seven Gerbert’s letters dedicated to mathematics.
First five of them were addressed to Gerbert’s friend, co-operator and perhaps pupil Constantine of Fleury. All letters to Constantine were written by the end of the 70-ties or at the beginning of the 80-ties of the 10th century, therefore during the time when Gerbert worked as teacher in Reims. Letter 1 is reaction to the period debate on conversion of three-membered numerical sequences arranged according to a certain ratio in the three same sums. Gerbert, following Boethius’s Introduction to arithmetic, deals with a conversion of superparticular numbers arranged in ratio 5:4 to a parity, i.e. ratio 1:1 and vigorously delimits the non-systematic method that was probably commonly used, however without respecting the nature of numbers, metaphysical hierarchy of relationships between the numerical ratios and ignoring the Boethius’s rules of conversions. Numerous and clear rejection of alternative approach of the ratios conversion is not even reduced by mathematical final correctness of the unrecognized method.
Letters 2 and 3 represent Gerbert’s commentaries on various text passages of Boethius’s Introduction to music. Boethius’s work is always quoted at first then Gerbert explains the arithmetic base of the quoted postulate. In Letter 2 Gerbert targets multiplication of ratios and classification of resulting products according to relative nature of numbers. Letter 3 describes and by using specific example clarifies a process of subtraction of smaller superparticular ratio from immediately subsequently bigger superparticular ratio. The resulting difference was found smaller then half of the subtracted ratio (subtrahend) as the double quantity of the result is a semitone smaller then subtracted ratio.
While the first three Gerbert’s letters are dedicated to theoretical arithmetic, Letters 4 and 5 represent an accompanying text of an abacist tract. Their subject is introduction to practical arithmetic, i.e. computing. Both abacist letters have very similar structures: Gerbert praises Constantine for his interest in study; and more he calls him consolation of his struggle and reason for writing the abacist treatises. Then Gerbert delimits himself towards other period scholars who only mention the abacus computations, however Gerbert criticises them for their disinterest in scientific texts of older authorities as well as for inability to understand neither the basic principles of abacus numeration nor methods of arithmetic computations.
Another two Gerbert’s mathematic letters were written in later period of Gerbert’s life (Letter 6 in year 988, Letter 7 probably in year 999). Both are part of a correspondence between Gerbert and Remigius of Trier (Letter 6) and Adelbold of Utrecht (Letter 7). First of the two letters deals in its mathematic part with divisible numbers, i.e. with way of measuring one number by another one. This topic is also linked to abacus numeration as well as to disintegration of numbers according to superparticular ratios. Letter 7 in general manner as well as with help of the specific examples explains different method of expressing the surface area of equilateral triangle using geometric and mathematic skill.
Individual letters are accompanied by commentaries closely introducing mainly the historical context of the individual problem and mathematic method presented in Gerbert’s letters.
The book opens an introductory study in order to ease orientation in the topics targeted by Gerbert’s mathematic letters as well as to closely present Boethius’s Introduction to arithmetic, the theoretical base of arithmetic knowledge initial for Gerbert’s texts (especially a character of number as such, character of numbers in relation to other numbers, i.e. above all number measuring or numeral sequences and ratios, further long also figural numbers and their discovering and depicting). Early medieval abacus computing tradition is also briefly presented including the design and structure of this unique mathematic device.
The introduction to theoretical and practical arithmetic is preceded by condensed description of Gerbert’s personality. The author of the letters is mainly presented as an important scholar of his period who was also very active in field of diplomacy. The book doesn’t miss out so called Gerbert’s legend reflecting already during the medieval period the personality of the great intellectual and mathematician.
Dating two medieval papal documents from the funds of the Moraviam Land Archive in Brno. A contribution to the history the Augustinian Eremites and the Cistercian Monastery in Velehrad.
The contribution focuses on two papal letters addressed to two different monastic institutions, whose dating in archive inventaries, as preserved in the editions, remains spurious. The documents are not connected and their thematic bond lies in the institu- tional position of their publisher and in the questions related to their uncertain dating. The study aims to prove, based on the diplomatic-paleographic analysis and material study, that the traditionally acepted dates need to be adjusted and both documents must be placed within their probable chronological context.