In Borrelli A., Hon G., and Zik Y., (editors). Giambattista Della Porta (1535–1615): A Reassessment. Archimedes, Vol. 44, 2017
In Bk. 17, Ch. 4 of Magia Naturalis (1589) Giambattista Della Porta (ca.
1535–1615) reported his... more In Bk. 17, Ch. 4 of Magia Naturalis (1589) Giambattista Della Porta (ca.
1535–1615) reported his experiments on concave spherical mirrors arranged in various setups. Della Porta identified two critical points: (1) the point of inversion (punctum inversionis) in reference to the place where the magnified image is turned upside down and seen blurred, and (2) the point of burning (punctum incensionis) in reference to the place where the reflected rays concentrate and ignite fire. Opticians and practitioners of the time distinguished between the two points but considered them to occupy the same spatial location.
Della Porta inferred from his studies of concave spherical mirrors that the position of the point of inversion and that of the point of burning occupy different spatial locations. He associated the point of inversion with a locus where the image is seen magnified, turned upside down and blurred—a matter of visual perception. He defined the point of burning as a physical, optical position associated with a geometrical point in which the converging rays ignite fire. Consequently, throughout Bk. 17, Della Porta discarded the point of inversion from his optical nomenclature and referred only to the point of burning, the real—so to speak—optical point. In so doing, Della Porta contributed fundamentally towards the technological management of sets of optical elements.
In this paper we follow the experimental practice of Della Porta as presented by the optical demonstrations in Bk. 17, Ch. 4. We discuss the theoretical principles Della Porta developed to clarify whether his claim concerning concave spherical mirror is hypothetical or was it based on an inference from experience. We offer novel insights into the development of the theory of reflection in concave spherical mirrors as it was pursued by Della Porta. He eliminated perceptual considerations from his optics and considered only geometrical-physical aspects. This approach was most useful in the development of the telescope where the critical aspect is not perception but rather ratio of spatial angles.
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between reflection in concave spherical mirror and refraction in glass sphere. We juxtapose these two studies and draw several philosophical lessons from the comparison between these two practices with a view to throwing into relief the fundamental differences in their respective conceptions of optics.
commonly held that it was Kepler who fathomed the principles of this instrument and
provided its first theoretical understandings. Galileo did not leave any analytical optical
treatise. He merely reported on his revolutionary astronomical findings in letters and
essays, so the standard historical observation goes, and did not present any theoretical
analysis of the instrument. In this paper we will examine Galileo's astronomical and
optical practice and try to see Galileo the scientist through the current sociological and
epistemological discussions.
The very invention of an instrument exerts a relationship between symbols and the
theories within which it is employed. For Galileo it was clear that in order to measure and interpret natural phenomena correctly he needed to develop an appropriate method that makes use of instrumentation. It is therefore instructive to regard the scientific instrument at the heart of Galileo’s enterprise – the telescope – in this light and examine the linkage Galileo established between theory, method and instrument.
This state of affairs offers a promising path along which the affinity and interrelations of theory, instrument, and progress in scientific knowledge can be examined. Therefore, through an exploratory inquiry into the role of these instruments, it would seem instructive to see first how Kepler’s reasoning led him to design new instruments. Second, on the basis of that knowledge, we may try to gain an understanding of how Kepler introduced instruments into his practice of science making them key ‘players’ in revolutionizing scientific thinking.
1535–1615) reported his experiments on concave spherical mirrors arranged in various setups. Della Porta identified two critical points: (1) the point of inversion (punctum inversionis) in reference to the place where the magnified image is turned upside down and seen blurred, and (2) the point of burning (punctum incensionis) in reference to the place where the reflected rays concentrate and ignite fire. Opticians and practitioners of the time distinguished between the two points but considered them to occupy the same spatial location.
Della Porta inferred from his studies of concave spherical mirrors that the position of the point of inversion and that of the point of burning occupy different spatial locations. He associated the point of inversion with a locus where the image is seen magnified, turned upside down and blurred—a matter of visual perception. He defined the point of burning as a physical, optical position associated with a geometrical point in which the converging rays ignite fire. Consequently, throughout Bk. 17, Della Porta discarded the point of inversion from his optical nomenclature and referred only to the point of burning, the real—so to speak—optical point. In so doing, Della Porta contributed fundamentally towards the technological management of sets of optical elements.
In this paper we follow the experimental practice of Della Porta as presented by the optical demonstrations in Bk. 17, Ch. 4. We discuss the theoretical principles Della Porta developed to clarify whether his claim concerning concave spherical mirror is hypothetical or was it based on an inference from experience. We offer novel insights into the development of the theory of reflection in concave spherical mirrors as it was pursued by Della Porta. He eliminated perceptual considerations from his optics and considered only geometrical-physical aspects. This approach was most useful in the development of the telescope where the critical aspect is not perception but rather ratio of spatial angles.
This paper will shed new light upon and clarifies the empirical working methods and the extent of Galileo’s knowledge of the optical principles involved in the construction of the telescope.
relies on instruments that serve as mediators between the world and the
senses. Instruments came in the shape of Heron’s Dioptra, Levi Ben Gerson’s
Cross-staff, Egnatio Danti’s Torqvetto Astronomico, Tycho’s Quadrant, Galileo’s
Geometric Military Compass, or Kepler’s Ecliptic Instrument. At the
beginning of the seventeenth century, however, it was unclear how an instrument
such as the telescope could be employed to acquire new information and
expand knowledge about the world. To exploit the telescope as a device for astronomical observations Galileo had to:
1. establish that telescopic images are not optical defects, imperfections in the
eye of the observer, or illusions caused by lenses;
2. develop procedures for systematically handling errors that may occur during
observation and measurement and methods of processing data.
Galileo made it clear that in order to measure and interpret natural phenomena
accurately, a suitable method and instrument would need to be developed. It is intriguing, therefore, to regard the Galilean telescope in this light and to discover the linkage established by Galileo among theory, method, and instrument—the telescope. Although the telescope was not invented through science, it is instructive to see how Galileo used optics to employ a theory-laden instrument for bridging the gulf between picture and scientiªc language, between drawing and reporting physical facts, and between merely sketching the world and actually describing it.
discussed, inter alia, the problem of the pinhole camera. Maurolyco outlined a
framework based on Euclidean geometry in which he applied the rectilinear
propagation of light to the casting of shadow on a screen behind a pinhole. We
limit our discussion to the problem of how the image behind an aperture is
formed, and follow the way Maurolyco combined theory with instrument to solve
the problem of the projection of light through small apertures. We show that
Maurolyco not only reformed the classical sources which, he thought, were no
longer the authoritative code of textual knowledge, but also established with the
dioptra a novel linkage of method, theory, and instrument. He thereby
demonstrated the importance of optics to the science of astronomy.
Books by Yaakov Zik
between reflection in concave spherical mirror and refraction in glass sphere. We juxtapose these two studies and draw several philosophical lessons from the comparison between these two practices with a view to throwing into relief the fundamental differences in their respective conceptions of optics.
commonly held that it was Kepler who fathomed the principles of this instrument and
provided its first theoretical understandings. Galileo did not leave any analytical optical
treatise. He merely reported on his revolutionary astronomical findings in letters and
essays, so the standard historical observation goes, and did not present any theoretical
analysis of the instrument. In this paper we will examine Galileo's astronomical and
optical practice and try to see Galileo the scientist through the current sociological and
epistemological discussions.
The very invention of an instrument exerts a relationship between symbols and the
theories within which it is employed. For Galileo it was clear that in order to measure and interpret natural phenomena correctly he needed to develop an appropriate method that makes use of instrumentation. It is therefore instructive to regard the scientific instrument at the heart of Galileo’s enterprise – the telescope – in this light and examine the linkage Galileo established between theory, method and instrument.
This state of affairs offers a promising path along which the affinity and interrelations of theory, instrument, and progress in scientific knowledge can be examined. Therefore, through an exploratory inquiry into the role of these instruments, it would seem instructive to see first how Kepler’s reasoning led him to design new instruments. Second, on the basis of that knowledge, we may try to gain an understanding of how Kepler introduced instruments into his practice of science making them key ‘players’ in revolutionizing scientific thinking.
1535–1615) reported his experiments on concave spherical mirrors arranged in various setups. Della Porta identified two critical points: (1) the point of inversion (punctum inversionis) in reference to the place where the magnified image is turned upside down and seen blurred, and (2) the point of burning (punctum incensionis) in reference to the place where the reflected rays concentrate and ignite fire. Opticians and practitioners of the time distinguished between the two points but considered them to occupy the same spatial location.
Della Porta inferred from his studies of concave spherical mirrors that the position of the point of inversion and that of the point of burning occupy different spatial locations. He associated the point of inversion with a locus where the image is seen magnified, turned upside down and blurred—a matter of visual perception. He defined the point of burning as a physical, optical position associated with a geometrical point in which the converging rays ignite fire. Consequently, throughout Bk. 17, Della Porta discarded the point of inversion from his optical nomenclature and referred only to the point of burning, the real—so to speak—optical point. In so doing, Della Porta contributed fundamentally towards the technological management of sets of optical elements.
In this paper we follow the experimental practice of Della Porta as presented by the optical demonstrations in Bk. 17, Ch. 4. We discuss the theoretical principles Della Porta developed to clarify whether his claim concerning concave spherical mirror is hypothetical or was it based on an inference from experience. We offer novel insights into the development of the theory of reflection in concave spherical mirrors as it was pursued by Della Porta. He eliminated perceptual considerations from his optics and considered only geometrical-physical aspects. This approach was most useful in the development of the telescope where the critical aspect is not perception but rather ratio of spatial angles.
This paper will shed new light upon and clarifies the empirical working methods and the extent of Galileo’s knowledge of the optical principles involved in the construction of the telescope.
relies on instruments that serve as mediators between the world and the
senses. Instruments came in the shape of Heron’s Dioptra, Levi Ben Gerson’s
Cross-staff, Egnatio Danti’s Torqvetto Astronomico, Tycho’s Quadrant, Galileo’s
Geometric Military Compass, or Kepler’s Ecliptic Instrument. At the
beginning of the seventeenth century, however, it was unclear how an instrument
such as the telescope could be employed to acquire new information and
expand knowledge about the world. To exploit the telescope as a device for astronomical observations Galileo had to:
1. establish that telescopic images are not optical defects, imperfections in the
eye of the observer, or illusions caused by lenses;
2. develop procedures for systematically handling errors that may occur during
observation and measurement and methods of processing data.
Galileo made it clear that in order to measure and interpret natural phenomena
accurately, a suitable method and instrument would need to be developed. It is intriguing, therefore, to regard the Galilean telescope in this light and to discover the linkage established by Galileo among theory, method, and instrument—the telescope. Although the telescope was not invented through science, it is instructive to see how Galileo used optics to employ a theory-laden instrument for bridging the gulf between picture and scientiªc language, between drawing and reporting physical facts, and between merely sketching the world and actually describing it.
discussed, inter alia, the problem of the pinhole camera. Maurolyco outlined a
framework based on Euclidean geometry in which he applied the rectilinear
propagation of light to the casting of shadow on a screen behind a pinhole. We
limit our discussion to the problem of how the image behind an aperture is
formed, and follow the way Maurolyco combined theory with instrument to solve
the problem of the projection of light through small apertures. We show that
Maurolyco not only reformed the classical sources which, he thought, were no
longer the authoritative code of textual knowledge, but also established with the
dioptra a novel linkage of method, theory, and instrument. He thereby
demonstrated the importance of optics to the science of astronomy.