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<div style="font-size: 13.3333330154419px;"><span style="font-size: 10pt; line-height: 15.3333320617676px; font-family: 'Segoe UI', sans-serif;">Sayin Liste Uyeleri,</span><br>
<br>
GTU Matematik Bölümü Genel Seminerleri kapsamında,<br>
08 Mayıs Cuma günü saat 15:00'da <span style="font-size: 13.3199996948242px;">David PİERCE</span><br>
(Mimar Sinan Güzel Sanatlar Universitesi) Moleküler Biyoloji</div>
<div style="font-size: 13.3333330154419px;">ve Genetik Bölümü konferans salonunda bir seminer</div>
<div style="font-size: 13.3333330154419px;">verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler davetlidir.<br>
<br>
Saygılarımızla,</div>
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<div style="background-color: white;"><font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">Title: The Sense of Proportion in Euclid</span></font><br style="font-size: 13.3199996948242px;">
<br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">Abstract: </span></font><font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">A proportion is an identification of ratios. In
the Elements, Euclid</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">(c. 300 b.c.e.) gives two definitions of a proportion: a clear</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">definition for arbitrary magnitudes, and an unclear definition for</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">numbers. A positive real number, as defined by Richard Dedekind</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">(1831--1916), can be understood as a ratio of magnitudes in Euclid's</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">sense. However, unlike Euclid, Dedekind establishes the *existence*</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">of all of the so-called real numbers: this has been overlooked, at</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">least by some of Dedekind's contemporaries. It has also been thought</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">that Euclid's ratios of numbers are just fractions in the modern</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">sense; but this makes Euclid wrong in ways that he is not likely to</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">be wrong. Euclid is *more* careful than we often are today</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">with the foundations of number theory. He proves rigorously that in</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">an ordered ring whose positive elements are well-ordered,</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">multiplication is commutative. Seeing this can be helped by treating</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">the reading of Euclid as an instance of doing history: history in the</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">sense worked out by the philosopher and historian R. G. Collingwood</span></font><br style="font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">(1889--1943) in </span></font><font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">several of his book</span></font></div>
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<div style="font-size: 13.3333330154419px;"><span style="font-size: 10pt; line-height: 15.3333320617676px; font-family: 'Segoe UI', sans-serif;">Dear all,</span><br>
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There will be a seminar in Gebze Technical University (GTU) on 8th of<br>
May by <span style="font-size: 13.3199996948242px;">David PİERCE </span>(MSGSU) <br>
Time and place: At 15:00 in Department of Molecular Biology and,<br>
Genetic, Building C, Auditorium.</div>
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<div style="font-size: 13.3333330154419px;"><font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">Title: The Sense of Proportion in Euclid</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">Abstract: </span></font><font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">A proportion is an identification of ratios. In
the Elements, Euclid</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">(c. 300 b.c.e.) gives two definitions of a proportion: a clear</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">definition for arbitrary magnitudes, and an unclear definition for</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">numbers. A positive real number, as defined by Richard Dedekind</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">(1831--1916), can be understood as a ratio of magnitudes in Euclid's</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">sense. However, unlike Euclid, Dedekind establishes the *existence*</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">of all of the so-called real numbers: this has been overlooked, at</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">least by some of Dedekind's contemporaries. It has also been thought</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">that Euclid's ratios of numbers are just fractions in the modern</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">sense; but this makes Euclid wrong in ways that he is not likely to</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">be wrong. Euclid is *more* careful than we often are today</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">with the foundations of number theory. He proves rigorously that in</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">an ordered ring whose positive elements are well-ordered,</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">multiplication is commutative. Seeing this can be helped by treating</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">the reading of Euclid as an instance of doing history: history in the</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">sense worked out by the philosopher and historian R. G. Collingwood</span></font><br style="font-family: Arial; font-size: 13.3199996948242px;">
<font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">(1889--1943) in </span></font><font face="Segoe UI,Helvetica,Arial,sans-serif" size="1"><span style="font-size: 13.31px;">several of his book</span></font></div>
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