The philosopher Immanuel Kant writes in the popular introduction to his philosophy: "There is no single book about metaphysics like we have in mathematics. If you want to know what mathematics is, just look at Euclid's Elements." (Prolegomena Paragraph 4) Even if the material covered by Euclid may be considered elementary for the most part, the way in which he presents essential features of mathematics in a much more general sense, has set the standards for more than 2000 years. He displays the axiomatic foundation of a mathematical theory and its conscious development towards the solution of a specific problem. We see how abstraction works and how it enforces the strictly deductive presentation of a theory. We learn what creative definitions are and how the conceptual grasp leads to the classification of the relevant objects. For each of Euclid's thirteen Books, the author has given a general description of the contents and structure of the Book, plus one or two sample proofs. In an appendix, the reader will find items of general interest for mathematics, such as the question of parallels, squaring the circle, problem and theory, what rigour is, the history of the platonic polyhedra, irrationals, the process of generalization, and more. This is a book for all lovers of mathematics with a solid background in high school geometry, from teachers and students to university professors. It is an attempt to understand the nature of mathematics from its most important early source.

Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.

Dies Skript enthalt den Standards toff der Linearen Algebra, wie er in den ersten Semestern ublich ist. Es wurde in verschiedenen Formen zu Vorlesungen herausgegeben, die ich fur Studenten der Mathematik, Physik und Informatik an der Technischen Hochschule Darmstadt gehalten habe. Ich habe mir Muhe gegeben, den Text so einfach und leicht zuganglich wie moeglich zu schreiben und jeweils typische Beispiele zu finden, um Satze und Begriffe zu illustrieren. Die Lineare Algebra kann man unter drei Aspekten sehen: geometrisch im Sinne der analytischen Geometrie, arithmetisch wie bei den Linearen Gleichungssystemen und vielen Teilen der Matrizenrechnung, die fur die Numerik wichtig sind, und schliesslich strukturbetont-abstrakt in der linearen und bilinearen Theorie der Vektorraume. Alle drei Aspekte soll- ten in einer Einfuhrung zur Geltung kommen, so auch in diesem Skript. Allerdings habe ich versucht, die begriffliche Behandlung eines Stoffes so weit wie moeglich ans Ende der jeweiligen Paragraphen zu stellen, um vorher uber Geometrie und Arithmetik eine verlassliche Intuition fur den Gegenstand aufzubauen. Diesem Zweck dienen besonders die einfuhrenden 2 Abschnitte uber die geometrischen Verhaltnisse im E . Gerade hier hat der Student, der ja die weitere Theorie noch nicht uberblicken kann, die Gelegenheit, aus der anschaulichen Fundierung den Sinn und die Be- deutung der Begriffe und Fragestellungen zu begreifen und damit von einer vernunftigen Basis aus weiterzuarbeiten.

Electrical Measuring Instruments
a Complete Catalogue of Electrical Measuring and Test Instruments
Hartmann & Braun
This edition of our catalogue is far larger than our previous issues. Our endeavours to keep pace with all the improvements in Science and Practice, and our wish to facilitate the selection of the most suitable instrument for whatever purpose required, by furnishing a slight description of the necessary manipulation, have led to this increase; which we hope will cause this catalogue to serve as a book of reference when using the instruments described.
With the exception of the copies of Standards of the Imperial Physico-Technical Laboratory, nearly all our instruments have been entirely designed by our firm and their associates. The usual standard types of apparatus have been remodelled and improved, to bring them up to the present day requirements for measuring instruments. Some of Prof. Kohlrausch's valuable designs have also been remodelled in accordance with his suggestions; we have always made it our special endeavour in improving and remodelling our instruments, to make them as simple and convenient as possible, so that they may be used by comparatively unskilled hands without loss of time; and for this reason we have originated several direct reading instruments, to which we would especially draw the attention of all practical engineers.
Especial care is given to the calibration, adjustment and exact determination of Constants, for which purpose we have a very complete and carefully designed plant, comprising 4 Dynamos for direct currents up to 1500 amperes, three sets of large accumulators and one set of several hundred small ones also capable of discharging at the rate of 2000 amperes and at potentials up to 800 volts, in addition to a direct current motor transformer for potentials up to 2000 volts and electrostatic arrangements for higher potentials. For alternating current work within very wide limits, an alternating current dynamo with 3 transformers having a range up to 1000 amps and 10000 volts is employed.
Whilst using our very best endeavours to meet all the requirements of accuracy, convenience, and mechanical perfection in design, it will still sometimes occur that every day use of our instruments will suggest points in which improvements are possible; and we shall be extremely obliged for any such suggestions.
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