On Euclid's Elements Book V, definition 5

It is well known fact that there are two definitions of proportion in Euclid's Elements: Book V, def. 5 and Book VII, def. 20. In the present paper we show that three different interpretations of definition V.5 can be given as modern notation is used: two of them arise from different readings of the definition itself, the third is a negation of disproportion (V, def. 7).It is well known fact that there are two definitions of proportion in Euclid's Elements: Book V, def. 5 and Book VII, def. 20. In the present paper we show that three different interpretations of definition V.5 can be given as modern notation is used: two of them arise from different readings of the definition itself, the third is a negation of disproportion (V, def. 7)

Metafizyka ruchu w Geometrii Kartezjusza

In Book II of The Geometry, Descartes distinguishes some special lines, which he calls geometrical curves. From the mathematical perspective, these curves are identified with polynomials of two variables. In this way, curves, which were understood as continuous quantities in Greek mathematics, turned into objects composed of points in The Geome- try. In this article we present assumptions which led Descartes to this radical change of the concept of curve

Cantor on Infinitesimals. Historical and Modern Perspective

In his 1887's Mitteilungen zur Lehre von Transfiniten, Cantor seeks to prove inconsistency of infinitesimals. We provide a detailed analysis of his argument from both historical and mathematical perspective. We show that while his historical analysis are questionable, the mathematical part of the argument is false

Podwójna negacja w B 2 poematu Parmenidesa

In our article we focus on an analysis of the structure of double negation in the poem of Parmenides,paying attention to the fragment B 2. The starting point for the analysis is the classificationof varieties of negation contained in Diogenes Laertius (VII.69-70): negation, denial,privation and double negation. We provide an example of double negation as given by Diogenes: “Not (is not a day) ↔ it is a day”. In terms of the poetic expression the law of double negationserves to strengthen the goddess’ speech. However, in the context of Parmenides’ ontology, thelaw of double negation serves as an affirmation of “is”. Our goal is to give a detailed analysis ofthe structure of double negation. In the next step we introduce Euclid’s proofs by comparison.We show that all four forms of negation indicated by Diogenes occur in the Elements and thereis a richer set of the linguistic forms used as an expression of negation, including that of doublenegation. Finally, we show that Parmenides applies consciously the law of double negation,and the poem is the first philosophical text confirming the use of this law. In short, doublenegation can be summarized as follows: for the Stoics, in Diogenes Laertius (VII.69-70): “not(is not a day) ↔ is a day”; for Euclid: “not (is not-equal) ↔ is equal” (Elements, I.6). “is notlike that (.... is not around ...) ↔ is around” (Elements VI.26); and in Parmenides: “is ↔ not(is not to be)” (B 2, v. 3)

Multidecadal (1960–2011) shoreline changes in Isbjørnhamna (Hornsund, Svalbard)

A section of a gravel-dominated coast in Isbjørnhamna (Hornsund, Svalbard) was analysed to calculate the rate of shoreline changes and explain processes controlling coastal zone development over last 50 years. Between 1960 and 2011, coastal landscape of Isbjørnhamna experienced a significant shift from dominated by influence of tide-water glacier and protected by prolonged sea-ice conditions towards storm-affected and rapidly changing coast. Information derived from analyses of aerial images and geomorphological mapping shows that the Isbjørnhamna coastal zone is dominated by coastal erosion resulting in a shore area reduction of more than 31,600 m2. With ~3,500 m2 of local aggradation, the general balance of changes in the study area of the shore is negative, and amounts to a loss of more than 28,000 m2. Mean shoreline change is −13.1 m (−0.26 m a−1). Erosional processes threaten the Polish Polar Station infrastructure and may damage of one of the storage buildings in nearby future