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The Latin music theorists

Boethius — the Friedlein volume: De institutione arithmetica, De institutione musica, and the Geometria (Teubner, 1867)

Gate passedSeeker and aboveModern transcription — not a facsimileBoethius · Guido AretinusPublic domain.15 segments · 143 pp

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1Google This is a digital copy of a book that was prcscrvod for gcncrations on library shclvcs bcforc it was carcfully scanncd by Googlc as part of a projcct to make the world's books discoverablc onlinc. It has survived long enough for the copyright to cxpirc and thc book to cntcr thc public domain. A public domain book is one that was never subjcct to copyright or whose legal copyright term has expircd. Whcthcr a book is in thc public domain may vary country to country. Public domain books are our gateways to the past, representing a wealth of history, cultuie and knowledge that's often difficult to discovcr. Marks, notations and other maiginalia present in the original volume will appear in this flle - a reminder of this book's long journcy from thc publishcr to a library and fmally to you. Usage guidelines Googlc is proud to partncr with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to thc public and wc arc mcrcly thcir custodians. Nevertheless, this work is expensive, so in order to keep providing tliis resource, we liave taken stcps to prcvcnt abusc by commcrcial partics, including placing lcchnical rcstrictions on automatcd qucrying. Wc also ask that you: + Make non-commercial use ofthefiles Wc dcsigncd Googlc Book Scarch for usc by individuals, and wc rcqucst that you usc thcsc filcs for personal, non-commercial purposes. + Refrainfivm automated querying Do nol send aulomatcd qucrics of any sort to Googlc's systcm: If you arc conducting rcscarch on machinc translation, optical character recognition or other areas where access to a laige amount of tcxt is hclpful, plcasc contact us. Wc cncouragc thc use of public domain materials for these purposes and may be able to help. + Maintain attributionTht GoogXt "watermark" you see on each flle is essential for informingpcoplcabout thisprojcct and hclping thcm lind additional materials through Google Book Search. Please do not remove it. + Keep it legal Whatcvcr your usc, rcmember that you are lesponsible for ensuring that what you are doing is legal. Do not assume that just bccausc wc bclicvc a book is in thc public domain for users in the United States, that the work is also in the public domain for users in other countrics. Whcthcr a book is still in copyright varies from country to country, and wc can'l offer guidance on whether any speciflc usc of any speciflc book is allowed. Please do not assume that a book's appearancc in Googlc Book Scarch mcans it can bc uscd in any manncr anywhere in the world.

2copyright varies from country to country, and wc can'l offer guidance on whether any speciflc usc of any speciflc book is allowed. Please do not assume that a book's appearancc in Googlc Book Scarch mcans it can bc uscd in any manncr anywhere in the world. Copyright infringement liabili^ can be quite severe. About Google Book Search Googlc's mission is to organizc thc world's information and to makc it univcrsally acccssiblc and uscful. Googlc Book Scarch hclps rcadcrs discovcr thc world's books whilc hclping authors and publishcrs rcach ncw audicnccs. You can scarch through thc full icxi of ihis book on thc wcb at|http://books.qooqle.com/| ,*. . ■*« /, ^i^ /•-' ' / ANICII MANLII TORQUATI SEVERINI k BOETII-i DE INSTITUTIONE AEITHMETICA LIBRI DUO I PE INSTITUTIONE MUSICA LIBRI QUINQUE. ACCEDIT GEOMETRIA QUAE FEUTUR BOETIf. E LIBRlS MANU SCRlPTIS EDIDIT GOBOFBEDUS PRIEDLEIN. LIPSIAE IN AEBIBUS B. G. TEUBNERI. MDCCCLXVir. LIPSIAE: TYPIS B. G. TEUBNERf. PRAEFATIO. "I Decem fere abhinc annos et scriptores latinos * cogniturus et rei mathematicae studiosus Boetio . l, coepi operam dare nec multo post acrius in mathe- l matica inprimis eius opera incumbendi auctor fuit j[| mihi Halmius,ad accuratius cognoscendam linguam 'j latinam hinc quoque aliquantulum afferri posse ratus. "7^ Prius tamen rebus arithmeticis utilem fructum afferre '1 i^ me posse putavi; quaeque inveneram publici iuris %^ feci libello de Boetii geometria edito^). Opiniones | meas aggressus est vir doctissimus Mauritius Can- tor^) meque inpulit, ut, quae minus recte de Boetii jf^ arte ratiocinandi et computandi statuerat, refellere ^ conarer argumentis quam maxime certis'^). Pauca , > etiam de geometria Boetii protuli^); quibus a Boetio eam profectam non esse comprobarem. M »'. i ^) Gerbert, die Geometrie des Boethius und die indischen 1 , Ziffern. Erlangen, Biasing 1861. | *) Mathematische Beitrage zum Kulturleben der Volkei', Halle, Schmidt 1863. 3) Zeitschrift fur Mathematik und Physik, IX, S. 73—95, U5— 171, 297—330. X, S. 241—282. 4) Neue Jahrbucher fur Philologie und Padagogik. 1863. S. ^26— 427. M y »? riM IV PKAEFATIO. Haec agentem interrogavit me Halmius, vel- lemne labores suscipere necessarios ad opera Boetii mathematica edenda, nec volentem tantum provo- cavit sed etiam libris manu scriptis quibus optimis potuit ad me missis simul adiuvit. Usus sum igitur codicibus Monachii asservatis praestantissimis , qui- bus accesserunt codices Bambergenses non minoris notae et liber Erlangensis, quem alter tantum codex Carnutensis aequat.

3d etiam libris manu scriptis quibus optimis potuit ad me missis simul adiuvit. Usus sum igitur codicibus Monachii asservatis praestantissimis , qui- bus accesserunt codices Bambergenses non minoris notae et liber Erlangensis, quem alter tantum codex Carnutensis aequat. Cuius rei gratiae milii agendae sunt maximae et Halmio ipsi et viris humanissi- mis et benevolentissimis Foringer^Thomas Mona- censibus, Stenglein Bambergensi, Autenrieth Erlangensi. Egregiam operam navavit mihi princeps Boncompagni, cuius summa liberalitate summa mea laude digna factum est, ut non solum, quae ipse in libris suis manu scriptis habuit, quae in aliis codicibus Romanis inventa sunt, quantum opus esse visum est, in meum usum possem convertere, sed etiam de codicibus, qui Neapoli, Florentiae, Veronae custodiuntur; fierem certior. Ita instructus rem aggredi ausus sum parum fortasse versans quid valerent humeri. Sed occasio- nem vircs intendendi omittere nohii. lam perfeci quae perficere mihi proposui. Utrumque Boetii opus et quod de arithmetica et quod de musica composuit, novissime apud nos anno 1570 Basileae editum, tribuB paene saeculis post rursus profero adiecto geometriae opusculo. De quibus pauca haec videntur monenda. Inscriptionem alterius operis Boetii sumpsi ex capite quarto libri I. de inst. mus. (p. 192, v. 19) : tn libris, quos de arithmeiica institudone conscripsimus, PRAEPATIO. V iinde titulum quoque petitum esse veri simile est, qui legitur in codice Bamb. HI. N. 13 (d) ante titulorum indicem libri II de inst. arithm. (p. 72, V. 9 var. lect.). Nec obstare mihi videtur, quod Boetius in cap. quadragesimo libri II inst. arithm. (p. 137, V. 7) arithmeticam introductionem se terminare dicit. Alterius operis inscriptionem manifestam reddi putavi cum capite decimo libri III. de inst. mus. (p. 283, V. 9): id, quod institutione musicae adorsi sumus, tum capite sextodecimo eiusdem libri III (p. 300, V. 2): quod superest musicae institutioni et eapite septimo libri V (p. 358, v. 2): quae secundo huius institutionis libro digessimus et infra (v. 9) ex sccundo huius institutionis musicae libro et quarto petendum est, Hinc eius opera, qui titulos finxit et indices eorum composuit, formula (e. g. p. 225, V. 16) de musica id est armonica institutione tiber orta videtur. Eorum librorum, quos Boetius de geometria scripsisse dicitur, investigare veram inscriptionem nihil aliud esset nisi operam et tempus perdere. lam inter homines doctos constat, eos libros minime Boetio tribuendos esse, quos codices manu scripti non pauci praeter duos illos praebent, qui in praestantissimis codicibus Erlangensi et Carnutensi reperiuntur^).

The source text as printed, transcribed diplomatically. Where the source language uses a non-Latin script that reaches us only through a Victorian romanisation, this layer is labelled transliteration, because that is what we hold.

primarypage 1

1Google This is a digital copy of a book that was prcscrvod for gcncrations on library shclvcs bcforc it was carcfully scanncd by Googlc as part of a projcct to make the world's books discoverablc onlinc. It has survived long enough for the copyright to cxpirc and thc book to cntcr thc public domain. A public domain book is one that was never subjcct to copyright or whose legal copyright term has expircd. Whcthcr a book is in thc public domain may vary country to country. Public domain books are our gateways to the past, representing a wealth of history, cultuie and knowledge that's often difficult to discovcr. Marks, notations and other maiginalia present in the original volume will appear in this flle - a reminder of this book's long journcy from thc publishcr to a library and fmally to you. Usage guidelines Googlc is proud to partncr with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to thc public and wc arc mcrcly thcir custodians. Nevertheless, this work is expensive, so in order to keep providing tliis resource, we liave taken stcps to prcvcnt abusc by commcrcial partics, including placing lcchnical rcstrictions on automatcd qucrying. Wc also ask that you: + Make non-commercial use ofthefiles Wc dcsigncd Googlc Book Scarch for usc by individuals, and wc rcqucst that you usc thcsc filcs for personal, non-commercial purposes. + Refrainfivm automated querying Do nol send aulomatcd qucrics of any sort to Googlc's systcm: If you arc conducting rcscarch on machinc translation, optical character recognition or other areas where access to a laige amount of tcxt is hclpful, plcasc contact us. Wc cncouragc thc use of public domain materials for these purposes and may be able to help. + Maintain attributionTht GoogXt "watermark" you see on each flle is essential for informingpcoplcabout thisprojcct and hclping thcm lind additional materials through Google Book Search. Please do not remove it. + Keep it legal Whatcvcr your usc, rcmember that you are lesponsible for ensuring that what you are doing is legal. Do not assume that just bccausc wc bclicvc a book is in thc public domain for users in the United States, that the work is also in the public domain for users in other countrics. Whcthcr a book is still in copyright varies from country to country, and wc can'l offer guidance on whether any speciflc usc of any speciflc book is allowed. Please do not assume that a book's appearancc in Googlc Book Scarch mcans it can bc uscd in any manncr anywhere in the world.

2copyright varies from country to country, and wc can'l offer guidance on whether any speciflc usc of any speciflc book is allowed. Please do not assume that a book's appearancc in Googlc Book Scarch mcans it can bc uscd in any manncr anywhere in the world. Copyright infringement liabili^ can be quite severe. About Google Book Search Googlc's mission is to organizc thc world's information and to makc it univcrsally acccssiblc and uscful. Googlc Book Scarch hclps rcadcrs discovcr thc world's books whilc hclping authors and publishcrs rcach ncw audicnccs. You can scarch through thc full icxi of ihis book on thc wcb at|http://books.qooqle.com/| ,*. . ■*« /, ^i^ /•-' ' / ANICII MANLII TORQUATI SEVERINI k BOETII-i DE INSTITUTIONE AEITHMETICA LIBRI DUO I PE INSTITUTIONE MUSICA LIBRI QUINQUE. ACCEDIT GEOMETRIA QUAE FEUTUR BOETIf. E LIBRlS MANU SCRlPTIS EDIDIT GOBOFBEDUS PRIEDLEIN. LIPSIAE IN AEBIBUS B. G. TEUBNERI. MDCCCLXVir. LIPSIAE: TYPIS B. G. TEUBNERf. PRAEFATIO. "I Decem fere abhinc annos et scriptores latinos * cogniturus et rei mathematicae studiosus Boetio . l, coepi operam dare nec multo post acrius in mathe- l matica inprimis eius opera incumbendi auctor fuit j[| mihi Halmius,ad accuratius cognoscendam linguam 'j latinam hinc quoque aliquantulum afferri posse ratus. "7^ Prius tamen rebus arithmeticis utilem fructum afferre '1 i^ me posse putavi; quaeque inveneram publici iuris %^ feci libello de Boetii geometria edito^). Opiniones | meas aggressus est vir doctissimus Mauritius Can- tor^) meque inpulit, ut, quae minus recte de Boetii jf^ arte ratiocinandi et computandi statuerat, refellere ^ conarer argumentis quam maxime certis'^). Pauca , > etiam de geometria Boetii protuli^); quibus a Boetio eam profectam non esse comprobarem. M »'. i ^) Gerbert, die Geometrie des Boethius und die indischen 1 , Ziffern. Erlangen, Biasing 1861. | *) Mathematische Beitrage zum Kulturleben der Volkei', Halle, Schmidt 1863. 3) Zeitschrift fur Mathematik und Physik, IX, S. 73—95, U5— 171, 297—330. X, S. 241—282. 4) Neue Jahrbucher fur Philologie und Padagogik. 1863. S. ^26— 427. M y »? riM IV PKAEFATIO. Haec agentem interrogavit me Halmius, vel- lemne labores suscipere necessarios ad opera Boetii mathematica edenda, nec volentem tantum provo- cavit sed etiam libris manu scriptis quibus optimis potuit ad me missis simul adiuvit. Usus sum igitur codicibus Monachii asservatis praestantissimis , qui- bus accesserunt codices Bambergenses non minoris notae et liber Erlangensis, quem alter tantum codex Carnutensis aequat.

3d etiam libris manu scriptis quibus optimis potuit ad me missis simul adiuvit. Usus sum igitur codicibus Monachii asservatis praestantissimis , qui- bus accesserunt codices Bambergenses non minoris notae et liber Erlangensis, quem alter tantum codex Carnutensis aequat. Cuius rei gratiae milii agendae sunt maximae et Halmio ipsi et viris humanissi- mis et benevolentissimis Foringer^Thomas Mona- censibus, Stenglein Bambergensi, Autenrieth Erlangensi. Egregiam operam navavit mihi princeps Boncompagni, cuius summa liberalitate summa mea laude digna factum est, ut non solum, quae ipse in libris suis manu scriptis habuit, quae in aliis codicibus Romanis inventa sunt, quantum opus esse visum est, in meum usum possem convertere, sed etiam de codicibus, qui Neapoli, Florentiae, Veronae custodiuntur; fierem certior. Ita instructus rem aggredi ausus sum parum fortasse versans quid valerent humeri. Sed occasio- nem vircs intendendi omittere nohii. lam perfeci quae perficere mihi proposui. Utrumque Boetii opus et quod de arithmetica et quod de musica composuit, novissime apud nos anno 1570 Basileae editum, tribuB paene saeculis post rursus profero adiecto geometriae opusculo. De quibus pauca haec videntur monenda. Inscriptionem alterius operis Boetii sumpsi ex capite quarto libri I. de inst. mus. (p. 192, v. 19) : tn libris, quos de arithmeiica institudone conscripsimus, PRAEPATIO. V iinde titulum quoque petitum esse veri simile est, qui legitur in codice Bamb. HI. N. 13 (d) ante titulorum indicem libri II de inst. arithm. (p. 72, V. 9 var. lect.). Nec obstare mihi videtur, quod Boetius in cap. quadragesimo libri II inst. arithm. (p. 137, V. 7) arithmeticam introductionem se terminare dicit. Alterius operis inscriptionem manifestam reddi putavi cum capite decimo libri III. de inst. mus. (p. 283, V. 9): id, quod institutione musicae adorsi sumus, tum capite sextodecimo eiusdem libri III (p. 300, V. 2): quod superest musicae institutioni et eapite septimo libri V (p. 358, v. 2): quae secundo huius institutionis libro digessimus et infra (v. 9) ex sccundo huius institutionis musicae libro et quarto petendum est, Hinc eius opera, qui titulos finxit et indices eorum composuit, formula (e. g. p. 225, V. 16) de musica id est armonica institutione tiber orta videtur. Eorum librorum, quos Boetius de geometria scripsisse dicitur, investigare veram inscriptionem nihil aliud esset nisi operam et tempus perdere. lam inter homines doctos constat, eos libros minime Boetio tribuendos esse, quos codices manu scripti non pauci praeter duos illos praebent, qui in praestantissimis codicibus Erlangensi et Carnutensi reperiuntur^).

The source text as printed, transcribed diplomatically. Where the source language uses a non-Latin script that reaches us only through a Victorian romanisation, this layer is labelled transliteration, because that is what we hold.

Commentary

whole issue ·

Historical[P-V]musica:1:2:001

Friedlein opens not with Boethius but with an argument about what is Boethius. The preface disputes whether the geometry books belong to him at all — "eos libros minime Boetio tribuendos esse" — cites Cantor's Mathematische Beiträge against himself, and leaves the question open: "sub iudice adhuc lis est", the case is still before the judge. He then names the Verona palimpsest as the manuscript that would settle it "si legi posset", if it could be read. An 1867 editor conceding in his own preface that his volume may contain a work by someone else is a better warrant than a confident attribution would be.

Historical[P-V]musica:1:3:001

The dedicatory epistle states the whole programme in one clause: what is offered is not gold but "quae ex Graecarum opulentia litterarum in Romanae orationis thesaurum sumpta conveximus" — what we have carried over from the wealth of Greek letters into the treasury of Roman speech. Boethius is describing a translation project, and he describes it as a transfer of wealth between treasuries rather than as authorship. Every claim this volume makes about number and sound is a claim he is relaying.

Cross-estate[I]musica:1:3:001

This house makes the same offer in the same terms — the original on the left, the carrying-across on the right — and it is worth noticing that the sixth-century version of it was also a compilation and said so. The epistle asks its dedicatee to "supervacua reseces, hiantia suppleas, errata reprehendas": cut what is superfluous, fill what gapes, reprehend what is wrong. That is an editorial brief, offered by the translator, before publication.