Elias AlIen (c.1588-1653) was known as the best mathematical instrument maker of his day. He lived and worked in London, creating a thriving business - he was the first English instrument maker to support himself solely through the production of instruments - and teaching his skills to many apprentices who became the core of the trade during the latter part of the century. My thesis provides a full biography of Allen, set within the framework of the community of people who were in some way connected to mathematics. The second part of the dissertation is devoted to the most important of Allen's instruments: the Gunter quadrant aqd Gilnter sector, and various of William Oughtred's designs - the circles of proportion; the horizontal instrument and double horizontal dial, and the universal equinoctial ring dial. These are described, their uses explained, and used as the base for discussions of the ways in which instruments influenced and were influenced by the development of mathematics. This section concludes with a catalogue of all the Allen instruments in British museums. As well as a comprehensive literature survey of the mathematical texts printed in England during Allen's lifetime, I have given considerable time to a 'reading' of the instruments themselves - through study of the originals, through production of my own versions, through reconstructions of the methods,of use, and, in the case of the sector, through computer analysis of the accuracy in use. The conclusion of my thesis is that the mathematical culture of seventeenth century England was far broader than that which is normally portrayed in histories of mathematics, involving a wide range of people with very different backgrounds and very different approaches to and understandings of mathematics. Above all, it is shown to be rooted strongly in a geometrical interpretation of mathematics and one which is inherently practical. In such a culture the role of instruments is fundamental and thus instrument makers like Elias Alien have a place at the heart of the mathematical community.

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2016-09-01T14:34:37Z No. of bitstreams: 1 Ana Rebeca Miranda Castillo.pdf: 4300226 bytes, checksum: 2a6d4a8336390def71101c782b5a7247 (MD5) / Made available in DSpace on 2016-09-01T14:34:37Z (GMT). No. of bitstreams: 1 Ana Rebeca Miranda Castillo.pdf: 4300226 bytes, checksum: 2a6d4a8336390def71101c782b5a7247 (MD5) Previous issue date: 2016-03-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work discourses about mathematical knowledge incorporated and mobilized in the construction and use of the staff (cross-staff), measuring instrument discussed in the treatise A Boke Named Tectonicon, written and published by Leonard Digges (1520-1559). Its objectives are: identifying the context in which the work and its author were inserted; checking from that context, what mathematical knowledge were mobilized and addressed in the treaty and its relation between mathematical practices and erudite knowledge from that time and analyze these mathematical knowledge added in staff, considering the practice of measurement and the procedures written by the author. Three analytical dimensions have been articulated, the historiography, the contextual and the epistemological and the study focused specifically on the construction and use of the staff (cross-staff). The social and political context of the 16th century has shown that the appreciation of mathematical knowledge it was a gradual result of social historical process occurred in England and promoted a rich dialogue among scholars of universities and craftsmen connected to different sectors of society. By reading and analyzing the treated, it was found how was made calculation of measure of a land area with several shapes and also calculation of measure of height of objects. Regarding the staff, it was observed that it was more than a simple measuring device, because in the process of its manufacture it was necessary a segment division of knowledge in equal parts, perpendicularity and demarcation scales. In its handling to achieve the desired measure it was necessary to mobilize the similarity of triangles property and to know that a line is determined by two points. And on its use the relative positions between the lines and orthogonal projections were skills that were implicit in making the measures. The results of this work concluded that both the staff and the other instruments addressed in Tectonicon, are more than simple tools, they are instruments that incorporate knowledge, they show the relation between to know and to do of an era and raises issues of epistemological to reflection on the construction of scientific and mathematical process / Este trabalho discorre sobre os conhecimentos matemáticos incorporados e mobilizados na construção e no uso do báculo (cross-staff), instrumento de medida abordado no tratado A Boke Named Tectonicon, escrito e publicado por Leonard Digges (1520-1559). Tem como objetivos: identificar o contexto no qual a obra e seu autor estavam inseridos; verificar, a partir desse contexto, quais conhecimentos matemáticos foram mobilizados e abordados no tratado e sua relação com as práticas matemáticas e o saber erudito da época além de analisar esses conhecimentos matemáticos incorporados no báculo, considerando a prática de mensuração e os procedimentos descritos pelo autor. Foram articuladas três dimensões de análise, a historiográfica, a contextual e a epistemológica e o estudo centrou-se especificamente na construção e uso do báculo (cross-staff). O contexto social e político do século XVI mostrou que a valorização do conhecimento matemático foi uma consequência gradual do processo histórico social ocorrido na Inglaterra e promoveu um rico diálogo entre os eruditos das universidades e artesãos ligados a diferentes setores da sociedade. Com a leitura e análise do tratado, verificou-se como era feito o cálculo de medida de área de terrenos com diversos formatos e também o cálculo da medida de altura de objetos. Em relação ao báculo, foi observado que era mais que um simples dispositivo de medição, pois já no processo de sua fabricação eram necessários conhecimentos de divisão de um segmento em partes iguais, perpendicularismo e demarcação de escalas. No seu manuseio, para obter a medida desejada, era necessário mobilizar a propriedade de semelhança de triângulos e saber que uma reta é determinada por dois pontos. E no seu uso posições relativas entre retas e projeções ortogonais eram conhecimentos que estavam implícitos ao fazer as medições. Com os resultados deste trabalho conclui-se que tanto o báculo como os outros instrumentos abordados em Tectonicon, são mais que simples ferramentas, são instrumentos que incorporam conhecimentos, mostram a relação entre o saber e o fazer de uma época e apontam questões de ordem epistemológica para reflexão a respeito do processo de construção do conhecimento científico e matemático