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EN
The paper emphasizes the role of ancient mathematics in the philosophical considerations in Pythagorean school and contains a reconstruction of some basic mathematical ideas giving reason for the explanation of many early-Pythagorean fragments. Some contributions to the discovery of incommensurability within Pythagorean school are presented. Their importance for mathematics cannot be overestimated. Then the course of mathematically oriented inquiries is set against some purely philological studies.
EN
Some of the things that are nowadays taken for granted in mathematics, namely that line segments of a certain length can be well ordered, and 'Euclidean' space is characterized by continuity and metricity, were problematic in antiquity. The main problem of ancient mathematics consisted in attempts to formulate anew a single mathematic theory after its disintegration into arithmetic and geometry caused by the discovery of incommensurability. Successive theories aimed at the metrization of geometric concepts and encompassed an ever increasing variety of mathematical objects. The paper proposes a new scheme of the development of ancient theories of proportion, which includes: 1. Early theories of proportion (P_1), among which two phases of development and two further subtypes have been distinguished in phase two: P_1a - early theories of numerical proportions and P_1b - early theories of geometrical proportions. 2. Theories of numerical proportions motivated by studies of irrational magnitudes: the theory of Archytas (P_2) and the theory of Theaetetus (P_3). 3. Theories of purely geometrical proportions P_4 (mainly book IV of Euclid's Elements) 4. The first theory of proportion that included mixed proportions, i.e. numerical and geometrical proportions (P_5). 5. Eudoxus' theory of proportions (P_6). The research of which the current paper presents the development of mathematics in a new light, and its results allow a reconstruction of the hermeneutic horizon for ancient mathematics.
PL
W pracy dokonano oceny i analizy szachownicy gruntów o układzie wstęgowym w miejscowości Brzeziny w gminie Puchaczów.Wykonano badania terenowe oraz zastosowano metodę kartograficzno-opisową. Badania obejmują działkę ewidencyjną określoną poprzez: powierzchnię, wydłużenie, kształt, dojazd do niej od zabudowy. Poznanie stanu badanej struktury przestrzennej gruntów pozwoliło na losowo-warstwowy wybór działek do szczegółowych analiz, tak aby proporcjonalnie do liczby działek w grupie obszarowej przypadło co najmniej 10% jej liczebności. Ogółem do badań szczegółowych przyjęto 226 ogólnej liczby działek. Największą wadliwością szczegółowo badanych działek jest ich nadmierne wydłużenie zwłaszcza w rejonie południowo-wschodnim miejscowości. Przeprowadzone badania dowodzą istnienia licznych wadliwości w strukturze przestrzennej gruntów badanych działek. Jest to następstwo przede wszystkim obrotu ziemią i sprawiedliwego dziedziczenia.Analiza struktury władania i użytkowania gruntów pozwoliła zauważyć, że w badanej miejscowości aż 96,7% gruntów należy do właścicieli indywidualnych natomiast 77% jej powierzchni to grunty orne. Około 25% badanych działek nie posiada dostępu do drogi publicznej. Dużym problemembadanej miejscowości jest wydłużenie działek, co wpływa negatywnie na opłacalność uprawy. Jedynym racjonalnym przedsięwzięciem, które mogłoby przebudować istniejący układ gruntów i zlikwidować ich nadmierne rozproszenie jest kompleksowe scalenie gruntów. Istotną przesłanką, która pozwala wytypować wieś Brzeziny do kompleksowego scalenia jest nadmierne rozdrobnienie i wydłużenie działek.
EN
In the paper were analysis and evaluation of plots patchwork in strip type in Brzeziny village, Puchaczów commune. Research was performed and was used to descriptive-research method. Studies include the registered parcel of land defined by: surface, elongation, shape, access to it from the building. Getting to know the atatus of the test spatial structure of land allowed for random-stratified selection of plots for detailed analysis so that in proportion to the number of parcels in the area group accounted for at least 10% of its numbers. In total, the research detailed adopted 226 the total number of plots. The greatest defect of the plots studied in detail is their excessive elongation particular region of south-east of the village. The studies prove the existence of many defects in the spatial structure of land in studied plots. This is primarily a consequence of land trading and fair inheritance. Analysis of the structureand ownershipof landletto note thatin the studyof the villageup96.7% of the land belongs toprivateownerswhile77% of its surface isarable land. Approximately 25% of the plotsdo not have accessto a public road. The big problemis theextension ofthe villagetestplots, which adversely affects theprofitability ofthe crop.The only rational way that could rebuild the existing layout of the land and eliminate their excessive disperse is a comprehensive consolidation of land. An important premise that let you to choose the Brzeziny village for a comprehensive consolidation is excessive fragmentation and elongation plots.
4
Content available remote Intuition and Hermeneutics: the Intuitive Analysis of Concepts
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EN
This paper presents certain aspect of intuitive reasoning in mathematics called the 'intuitive analysis of concepts' along some schemes of that kind of intuitive analysis. The method of the intuitive analysis of concept of polyhedra based on the historical findings as presented by Lakatos in 'Proofs and Refutations' is described. Some important consequences for phenomenology as well as philosophy and history of mathematics follow. Mathematical knowledge seems to be created within the 'hermeneutical horizon' distinct for ancient and modern mathematics.
EN
The article points out some mathematical facts relates to epistemology and takes them as an analogy opening a possibility of falsification of some general standpoints in theory of knowledge, such as epistemological antirealism, nominalism, etc.
7
Content available remote Revolution or Rebirth? Comments on 'The Forgotten Revolution' by Lucio Russo
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EN
This article presents some basic facts concerning ancient Greek mathematics which contradict many theses of 'The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had To Be Reborn'. The disastrous and distorting negation of existence of early Greek mathematics and its scientific achievements is commonly accepted in some related studies, e.g. on the Pythagoreans. The argument concerns also some problems in modern science and mathematics.
EN
The article is treating of a new interpretation of ancient geometry (part I) and is willing to explain several mathematical and historical conceptions that were presented in Pappus' 'Comment on the Xth Book of 'Elements' of Euclid' (part II). Euclid's 'Elements' were a kind of 'intuitive model', quite different from the contemporary one, divested of the 'infinite space' notion. Reconstruction of the hermeneutic horizon of the ancient mathematics allows us to explain the structure and mathematics presented in the columns of the Xth book of 'Elements'. The following subjects were handled: (1) reasons for elimination of the Euclid's 'infinite space' notion and substituting it for Plato's Diad in ancient times, (2) basing geometry and searches over the incommensurable magnitudes on one distinguished line together with mathematical consequences, (3) differences in the way of thinking of ancient and contemporary mathematician. Scientific studies allow to qualify from the historical point of view the share in development of the incommensurable magnitudes theories presented by Theaetetus of Athens, Apollonius of Perga, Euclid and Eudoxus. In the article a reconstruction of the mathematical contents of the lost Apollonius' treatise on incommensurable magnitudes is also presented A traditionally established pattern of the development of geometry, according to which Euclidean geometry used to extend as theory basing on relatively unalterable outfit of the fundamental intuition as, for instance, Euclid's infinite space, continuum intuitions and metric intuitions (what is important, the first revolutionary change was a discovery of non–Euclidean geometry in the 19th century) cannot be sustained.
10
Content available remote Platonism in Mathematics and the Platonism in Physical Science
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EN
Mathematical platonism has become an internal problem in mathematics which results in some strictly mathematical methods of the mathematical enquiry. These methods often tend to display not quite self-conscious treatment of the mathematical reality as given and already present. The mathematical platonism is not an innocent attitude and not merely a psychological add-on to the process of science creation but should become formulated explicity, especially in physical science. The presence of platonism in physics is briefly described and some consequences of the platonism are shown.
EN
Amangst 138 epiphytic bacterial isolates originating from hazel leaves 12 isolates limited the growth of B. cinerea, 33 limited the growth of C. corylicola, 31 inhibited the growth of G. coryli and 36 isolates showed antagonistic activity against Phomopsis sp. in-vitro. It was found that 9 isolates limited the growth of all the pathogenes tested and 7 isolates inhibited the growth of at least 3 out of them. The abilities of bacterial isolates tested to limit of the pathgenes growth were higher after 4 days of the biotic influence than after 8 days. Isolates of bacteria with the highest inhibitory activity against the above – mentioned pathogenes were identified as Pseudomonas fluorescens, Pseudomonas sp., Bacillus sp. and Enterobacter, Citobacter, Klebsiella or Erwinia cypripedii.
PL
Spośród 138 badanych izolatów bakterii epifitycznych pochodzących z liści leszczyny, 12 izolatów ograniczało in vitro wzrost kolonii Botrytis cinerea, 33 ograniczało wzrost Cytospora corylicola, 31 hamowało wzrost Gloeosporium coryli, a 36 wykazywało antagonistyczne oddziaływanie w stosunku do Phomopsis sp. Stwierdzono, że tylko 9 izolatów ograniczało wzrost kolonii wszystkich wymienionych patogenów, a 7 izolatów ograniczało wzrost przynajmniej 3 gatunków grzybów patogenicznych. Zdolność badanych izolatów bakterii do ograniczania wzrostu patogenów była większa po 4 dniach biotycznego oddziaływania, a po 8 dniach znacznie się zmniejszyła. Najefektywniejsze w ograniczaniu izolaty bakterii należały do rodzajów Pseudomonas fluorescens, Pseudomonas spp., Bacillus sp., Enterobacter, Citrobacter, Klebsiella lub Erwinia cypripedii.
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