### Abstract

Lingua originale | English |
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Titolo della pubblicazione ospite | From Logic to Practice |

Pagine | 3-21 |

Numero di pagine | 19 |

Stato di pubblicazione | Published - 2014 |

### Serie di pubblicazioni

Nome | Boston Studies in the Philosophy and History of Science |
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### Cita questo

*From Logic to Practice*(pagg. 3-21). (Boston Studies in the Philosophy and History of Science).

**A Geometrical Constructive Approach to Infinitesimal Analysis: Epistemological Potential and Boundaries of Tractional Motion.** / Milici, Pietro.

Risultato della ricerca: Chapter

*From Logic to Practice.*Boston Studies in the Philosophy and History of Science, pagg. 3-21.

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TY - CHAP

T1 - A Geometrical Constructive Approach to Infinitesimal Analysis: Epistemological Potential and Boundaries of Tractional Motion

AU - Milici, Pietro

PY - 2014

Y1 - 2014

N2 - Recent foundational approaches to Infinitesimal Analysis are essentially algebraic or computational, whereas the first approaches to such problems were geometrical. From this perspective, we may recall the seventeenth-century investigations of the “inverse tangent problem.” Suggested solutions to this problem involved certain machines, intended as both theoretical and actual instruments, which could construct transcendental curves through so-called tractional motion. The main idea of this work is to further develop tractional motion to investigate if and how, at a very first analysis, these ideal machines (like the ancient straightedge and compass) can constitute the basis of a purely geometrical and finitistic axiomatic foundation (like Euclid’s planar geometry) for a class of differential problems. In particular, after a brief historical introduction, a model of such machines (i.e., the suggested components) is presented. Then, we introduce some preliminary results about generable functions, an example of a “tractional” planar machine embodying the complex exponential function, and, finally, a didactic proposal for this kind of artifact.

AB - Recent foundational approaches to Infinitesimal Analysis are essentially algebraic or computational, whereas the first approaches to such problems were geometrical. From this perspective, we may recall the seventeenth-century investigations of the “inverse tangent problem.” Suggested solutions to this problem involved certain machines, intended as both theoretical and actual instruments, which could construct transcendental curves through so-called tractional motion. The main idea of this work is to further develop tractional motion to investigate if and how, at a very first analysis, these ideal machines (like the ancient straightedge and compass) can constitute the basis of a purely geometrical and finitistic axiomatic foundation (like Euclid’s planar geometry) for a class of differential problems. In particular, after a brief historical introduction, a model of such machines (i.e., the suggested components) is presented. Then, we introduce some preliminary results about generable functions, an example of a “tractional” planar machine embodying the complex exponential function, and, finally, a didactic proposal for this kind of artifact.

UR - http://hdl.handle.net/10447/105087

UR - http://link.springer.com/chapter/10.1007/978-3-319-10434-8_1

M3 - Chapter

SN - 978-3-319-10433-1

T3 - Boston Studies in the Philosophy and History of Science

SP - 3

EP - 21

BT - From Logic to Practice

ER -