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Chesapeake Partners, a Baltimore-based fund set up by Traci and Mark Chesapeake in the early s, thinks life might be easier as a family office.

Chesapeake follows a long line of other hedge funds turning themselves into family offices. A Bloomberg report said Peninsula bought a controlling stake in a Brazilian e-commerce wine company and also bought a bakery chain earlier this year. Kyriakos Mamidakis, the co-founder of Mamidoil-Jetoil, was found dead at his Athens home earlier this week, according to media reports.

Mamidakis, 84, founded the business with his two brothers, which at its height was one of the most successful petroleum trading companies in Greece and the Balkans. But the near collapse of the Greek economy in the last seven years took its toll on the business and Mamidoil-Jetoil filed for bankruptcy two days before Mamidakis death. Exclusive news, analysis, and research on global family enterprises and private investment offices. Before that, however, it needs pointing out that it is impossible to tackle all instances in which one encounters non sequiturs, misquotations, mistranslations, inaccurate enunciations of theorems, et cetera, in this challenging and wrongheaded book.

A few examples should suffice. To me there seems to be a contradiction between the claim that geometers at the Platonic Academy proved the truth of a whole chain of non-Euclidean propositions p. It actually precedes all five postulates. Euklid [] : This, needless to say, we must also do selectively. In our survey, we shall attempt to illustrate them all.

Jenkinson renders it basically in the same fashion. As it stands, it says nothing at all about geometry, and certainly nothing about non-Euclidean geometry. Now some things are naturally knowable through themselves, and others through something else for principles are knowable through themselves, while the examples which fall under the principles are knowable through something else ; and when any one tries to prove by means of itself that which is not knowable by means of itself, then he is begging the point at issue.

This may be done by directly postulating the proposition which is to be proved; but we may also have recourse to some other propositions of a sort which are of their very nature proved by means of our proposition, and prove the point at issue by means of them: e. This is exactly what those persons do who think that they are drawing parallel lines; for they do not realize that they are making assumptions which cannot be proved unless the parallel lines exist H. Aristotle []: Comparing Elements , I. Euclid would not have grasped the difference.

Aber ebenso wie Legendre von Saccheri, hat auch Saccheri keine Kenntnis von dieser Stelle der priora gehabt. Again, we cease our inquiry for the reason and assume we know it when we reach a fact whose existence does not depend upon any other fact […]. If, then, the same principle applies to all causes and reasoned facts, and if our knowledge of all final causes is most complete under the conditions which we have just described, then in all other cases too our knowledge is most complete when we reach a fact which does not depend further upon any other fact.

So when we recognize that the sum of the exterior angles of a figure is equal to four right angles, because the figure is isosceles, there still remains the reason why the figure is isosceles, viz. If this reason depends upon nothing else, our knowledge is now complete. Moreover our knowledge is now universal; and therefore universal knowledge is superior. Aristotle [] : The context of the passage is clear. It deals with the different meanings and cognitive status of the concepts possible, impossible, true, false, and it is in this context that the two impossible examples, of the triangle, whose internal angles are not together equal to 2R, and the diagonal of the square, which is commensurable with the side, are brought.

Again, impossible hypotheses bring in their wake impossible consequences. We can deal with only one example, but this suffices, as what shall be said about it is transferable, mutatis mutandis , to the rest. His conclusion, unwarranted to my mind by the textual evidence, is that in geometry, like in ethics, freedom of decision and choice reigns supreme that is, the Greek geometers were fully aware that it is up to them to choose which geometry to follow and develop, Euclidean or non-Euclidean, and that choice was completely, absolutely, free, and independent of any geometrical considerations!

But man is a first principle of a certain motion, for action is motion. And since as in other matters the first principle is a cause of the things that exist or come into existence because of it, we must think as we do in the case of demonstrations. For example, if as the angles of a triangle are together equal to two right angles the angles of a quadrilateral are necessarily equal to four right angles, that the angles of a triangle are equal to two right angles is clearly the cause of that fact; and supposing a triangle were to change, a quadrilateral would necessarily change too—for example if the angles of a triangle became equal to three right angles, the angles of a quadrilateral would become equal to six right angles, or if four, eight; also if a triangle does not change but is as described, a quadrilateral too must of necessity be as described.


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Hence if in fact there are among existing things some that admit of the opposite state, their first principles also must necessarily have the same quality. Aristotle [] : , The theme of the passage is the relation between archai , basic principles, and their consequences. When the archai change, their consequences change too and changed consequences lead necessarily to changed archai. Since the sum of the angles in a triangle is 2R, the necessary consequence is that the sum of internal angles in a quadrangle, composed of two triangles, is 4R.

Some Examples of Toth’s Historical Methodology

Should the first sum change to 3R, the latter too would change to 6R. The sum of the interior angles of a triangle is itself a consequence of other principles archai , primarily of the Fifth Postulate. That is all. And it is obvious that with regard to immovable things also, if one assumes that there are immovable things, there is no deception in respect of time. But that, friend Cratylus, is no answer.

In the Posterior Analytics 85b28—86a4, Aristotle treats the procedure for identifying the final cause, and says, inter alia: Again, we cease our inquiry for the reason and assume we know it when we reach a fact whose existence does not depend upon any other fact […].


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It has nothing to do with alternative geometries, nothing at all. Why does he do this?

The Quotable Rob Plummer

Presumably to be able to find a connection, even if a weak one, between this innocent statement and its non-Euclidean counterpart pp. I shall not repeat his quasi-arguments, which I find, needless to say, eminently unconvincing and blatantly anachronistic. What can one say to this? Let us take the passage from the Eudemian Ethics , b15—42, and see what it really says. Concerning the alleged freedom of the geometers to choose between a Euclidean and non-Euclidean geometry, there is nothing as such in this passage.

To take just one example, Metaphysica a4—7, this is what Aristotle actually says: And it is obvious that with regard to immovable things also, if one assumes that there are immovable things, there is no deception in respect of time. What he says about this passage on pages — is blatantly anachronistic, wild in its implications, and totally gratuitous.

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The crucial parts deal, indeed, with the distinction between consistency and truth, pointing out that a single small mistake in the course of a geometrical proof, may lead, if faultlessly pursued, to false, though correct, necessary consequences. Aristotle [] The Athenian Constitution. The Eudemian Ethics. On Virtues and Vices.

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Google Scholar. The Categories. On Interpretation. Prior Analytics. On the heavens. Posterior Analytics. Euclid [] With introduction and commentary by Thomas L. Second edition revised with additions. New York: Dover. Euklid [] Die Elemente. Heath, Thomas L.

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Mathematics in Aristotle. Oxford: Clarendon. Plato [] Edited by Edith Hamilton and Huntington Cairns.