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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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Windham Press is committed to bringing the lost cultural heritage
of ages past into the 21st century through high-quality
reproductions of original, classic printed works at affordable
prices.
This book has been carefully crafted to utilize the original images
of antique books rather than error-prone OCR text. This also
preserves the work of the original typesetters of these classics,
unknown craftsmen who laid out the text, often by hand, of each and
every page you will read. Their subtle art involving judgment and
interaction with the text is in many ways superior and more human
than the mechanical methods utilized today, and gave each book a
unique, hand-crafted feel in its text that connected the reader
organically to the art of bindery and book-making.
We think these benefits are worth the occasional imperfection
resulting from the age of these books at the time of scanning, and
their vintage feel provides a connection to the past that goes
beyond the mere words of the text.
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