A obra de triangulis omnimodis libri quinque de Johann Müller Regiomontanus (1436 1476): uma contribuição para o desenvolvimento da trigonometria

Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann Müller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician

Gerardi Joannis Vossii rhetorices contractae sive partitionum oratoriarum : libri quinque : editio juxta exemplar lipsiense quantum fieri potuit diligentissime correcta, & duplice indice locupletataed.juxta exemplar lipsiense quantum fieri potuit diligentissime correcta, & duplice indice locupletata

Gerardus Johannes Vossius, filólogo e erudito holandês, nasceu em Heidelberg em 1577 e morreu em Amsterdã em 1649. Em 1632, transferiu-se para Amsterdã onde ensinou história no então fundado Athenaeum. Suas obras mais notáveis são sobre as heresias dos historiadores antigos. ‘Rethorices contractae’ é uma obra produzida em 1606, que contém regras sobre retorica e oratória. Formada por cindo livros ou partes o autor apresenta a natureza, o gênero e os tipos de retórica, o uso de figuras de linguagens e o estilo dos discursos para emprego nas diversas situações. No final do livro, encontra-se o índice remissivo de assuntos.

1.° Codicis Theodosiani libri sexdecim ; sed ubi solas interpretationes, quae Breviario Aniani ab anonymo insertae sunt, reperias : praemittitur excerptum ex libro quinto etymologiarum Isidori. — 2.° Theodosii Junioris, Valentiniani III. Martiani, Majoriani et Severi novellae constitutiones. — 3.° Gaii Institutionum epitome. — 4.° Julii Pauli sententiarum libri quinque ; sed et hîc solae interpretationes Breviarii Aniani

Puteanus

1.° Codicis Theodosiani libri sexdecim ; et hîc solae interpretationes. — 2.° Theodosii Junioris, Valentiniani III. Marciani, Majoriani et Severi novellae constitutiones. — 3.° Gaii Institutionum epitome. — 4.° Julii Pauli sententiarum libri quinque, cum interpretationibus. — 5.° Excerpta ex Codicibus Gregoriano, Hermogeniano et Papianeo

Bigotianus

1.° Codicis Theodosiani libri sexdecim ; et hîc solae interpretationes. — 2.° Theodosii Junioris, Valentiniani III. Marciani, Majoriani et Severi novellae constitutiones. — 3.° Gaii Institutionum epitome : finis desideratur. — 4.° Julii Pauli sententiarum libri quinque, cum interpretationibus. — 5.° Excerpta ex Codicibus Gregoriano, Hermogeniano et Papianeo. — 6.° Excerpta ex libro quinto etymologiarum Isidori. — 7.° Canones secundi et tertii concilii Aurelianensis. — 8.° Fragmentum concilii Chalcedonensis, de Libertorum ordinationibus. — 9.° Fragmenta legum. — 10.° Edictum Imperatorum Marciani et Valentiniani III. de confirmatione concilii Chalcedonensis

Bigotianus

1.° Codicis Theodosiani libri quatuordecim posteriores ; et hîc solae interpretationes. — 2.° Theodosii Junioris, Valentiniani III. Martiani, Majoriani et Severi novellae constitutiones. — 3.° Gaii Institutionum epitome. — 4.° Julii Pauli sententiarum libri quinque, sed foliorum ordine turbato accedunt interpretationes. — 5.° Excerpta ex Codicibus Gregoriano, Hermogeniano et Papianeo. — 6.° Excerptum ex libro quinto Isidori etymologiarum

Colbertinus

historiae ecclesiasticae gentis Anglorum libri quinque : authore Beda, Presbytero ; praemittitur epitaphium discipulorum sex sancti Gregorii, Papae.

Colbertinus

1.° Historiae ecclesiasticae gentis Anglorum libri quinque : authore Beda, Presbytero. — 2.° Vita S. Nicolai, Episcopi Myrensis. — 3.° Fragmentum Eusebii de sanctis Polycarpo et Irenaeo.

Tellerianus

1.° Historiae ecclesiasticae gentis Anglorum libri quinque : authore Beda, Presbytero. — 2.° Vita sancti Gregorii, Papae.

Colbertinus

1.° Vita sancti Hilarii, Pictaviensis Episcopi : authore Fortunato, Episcopo. — 2.° Vita sancti Apri, Confessoris. — 3.° Vita sancti Geraldi, Confessoris. — 4.° Vita sancti Amandi, Episcopi : additum est à Milone, Monacho, ejusdem vitae supplementum. — 5.° Sermo legendus in transitu ejusdem sancti Amandi. — 6.° Vita sancti Apollinaris, Episcopi Valentini. — 7.° Passio sancti Antonini, Apamiensis Martyris. — 8.° Passio sancti Prisci, Episcopi. — 9.° Passio sanctorum Vivianae et Flaviani. — 10.° Passio sancti Theodoreti. — 11.° Passio sanctorum Primi et Feliciani. — 12.° Vitae sanctorum Firmini et Ferreoli, Episcoporum Uceciensium. — 13.° Historia persecutionis Africanae, sive Wandalicae sub Genserico et Hunnerico, Vandalorum Regibus : authore Victore, Vitensi Episcopo. — 14.° Historiae Longobardorum libri quinque : authore Paulo Diacono.

Colbertinus

consolationis philosophiae libri quinque : authore Boëtio ; passim inter lineas glossae et ad marginem scholia.

Philiberti de la Mare

Avicennae canonis libri quinque : interprete Gerardo, Carmonensi ; ad calcem subjiciuntur canonis synonyma.

Colbertinus