The “day of Brahman” in the work of Āryabhata

Summary In the astronomical treatise ryabhatya of ryabhata several verses are interpolated, namely all those verses in which either Brahman was mentioned or extremely large periods were introduced. The interpolator was known to AlBrn as ryabhata of Kusumapura, who belongs to the school of the elder ryabhata. The aim of the interpolator was to bring the teaching of the elder ryabhata into accordance with the revelation of Svayambh. Svayambh is another name for Brahm.     

Uptake of D-glucose anomers by rat retina

Summary Uptake ofd-glucose anomers by isolated rat retina was studied. After 3 min incubation at 37°C in the presence of or anomer (750 g/ml), a significantly greater uptake (1.32 mg/g wet tissue) of -anomer was observed compared with that of -d-glucose (1.11 mg/g wet tissue). This result and other data suggest that the carrier ford-glucose transport in the retina prefers the -anomer stereospecifically.Acknowledgment. The authors are grateful to Mr S. Suzuki for his technical assistance.     

Neue Gesichtspunkte zum 5. Buch Euklids

Summary The author's purpose is to read the main work of Euclid with modern eyes and to find out what knowledge a mathematician of today, familiar with the works of V. D. Waerden and Bourbaki, can gain by studying Euclid's theory of magnitudes, and what new insight into Greek mathematics occupation with this subject can provide.The task is to analyse and to axiomatize by modern means (i) in a narrower sense Book V. of the Elements, i.e. the theory of proportion of Eudoxus, (ii) in a wider sense the whole sphere of magnitudes which Euclid applies in his Elements. This procedure furnishes a clear picture of the inherent structure of his work, thereby making visible specific characteristics of Greek mathematics.After a clarification of the preconditions and a short survey of the historical development of the theory of proportions (Part I of this work), an exact analysis of the definitions and propositions of Book V. of the Elements is carried out in Part II. This is done word by word. The author applies his own system of axioms, set up in close accordance with Euclid, which permits one to deduce all definitions and propositions of Euclid's theory of magnitudes (especially those of Books V. and VI.).In this way gaps and tacit assumptions in the work become clearly visible; above all, the logical structure of the system of magnitudes given by Euclid becomes evident: not ratio — like something sui generis — is the governing concept of Book V., but magnitudes and their relation of having a ratio form the base of the theory of proportions. These magnitudes represent a well defined structure, a so-called Eudoxic Semigroup with the numbers as operators; it can easily be imbedded in a general theory of magnitudes equally applicable to geometry and physics.The transition to ratios — a step not executed by Euclid — is examined in Part III; it turns out to be particularly unwieldy. An elegant way opens up by interpreting proportion as a mapping of totally ordered semigroups. When closely examined, this mapping proves to be an isomorphism, thus suggesting the application of the modern theory of homomorphism. This theory permits a treatment of the theory of proportions as developed by Eudoxus and Euclid which is hardly surpassable in brevity and elegance in spite of its close affinity to Euclid. The generalization to a classically founded theory of magnitudes is now self-evident.

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Vorgelegt von J. E. Hofmann     

Geminus and the concept of mean motion in Greco-Latin astronomy

Conclusion Geminus account of lunar motion in chapter 18 of hisIntroductio astronomiae is, in our view, an important contribution to Greco-Latin astronomy because, in attempting to reconstruct arithmetically (the parameters of) the Moon's motion in longitude, he undermines the task astronomers had hitherto set for themselves. This undermining of a commonly acknowledged view of the purpose of astronomy is articulated in a whole new set of questions concerning the nature and place of both observation and mathematical reasoning in the science of the heavens. Yet, one must not overlook the fact thatGeminus reconstruction also indicates resources for addressing these questions. Of these resources, the most powerful proved to be the idea that irregular motion could be quantified as a systematic departure from a mean motion, and the idea that observational data could be organized and structured by means of genetic arithmetical reconstructions.But, since we limit our attention to extant treatises and decline to speculate about works or parts of works that have not survived, we must say that it would takePtolemy to discern the new direction for astronomy thatGeminus opened up and to pursue it. In part, this involved straightening out the conflated conception of mean motion in chapter 18 — the qua arithmetic mean daily displacement can only be anapparent lunar motion in longitude and not one the Moonreally makes, but the same need not be true of the qua periodic mean daily displacement — and determining its proper relation to real and apparent planetary motion. Indeed,Ptolemy's genius lay, we think, in seeing that even though, in assimilating Babylonian astronomy, earlier and contemporary Greco-Latin writers betrayed a confused, inconsistent, and unsophisticated grasp of the proper role of arithmetic, geometry, and observation in astronomical argument [seeBowen 1994], the solution lay in a mathematical reconstruction of the observed celestial motions, in which mean motion played an essential role.     

Funktion der Spermien in inkompatiblen Kreuzungen der StechmückeCulex pipiens L.

Summary After irradiating males of the incompatible crossC. pipiens Hamburg ×C. pipiens Paris with X-ray doses between 1 kR and 40 kR, it could be shown that in this cross the sperm has only the function of activating the egg. All the hybrid embryos develop from the haploid female pronucleus.Herrn Professor Dr.H. Laven danke ich für Unterstützung und wertvolle Diskussionen.     

Fucosidases du suc digestif d'Helix pomatia

Summary The-d-fucosidase and -l-fucosidase activities of digestive juice ofHelix pomatia have been studied.-d-fucosidase can be separated from-d-galactosidase by heat inactivation.     

The Kepler Problem from Newton to Johann Bernoulli

Summary Newton solved what was called afterwards for a short time the directKepler problem (le problème direct): given a curve (e.g. an ellipse) and the center of attraction (e.g. the focus), what is the law of this attraction ifKepler's second law holds?The problème inverse (today: the problème direct) was attacked system-atically only later, first byJacob Hermann, then solved completely byJohann Bernoulli in 1710 and followingBernoulli byPierre Varignon. How didBernoulli solve the problem? What method did he use for this purpose and which of his accomplishments do we still follow today?In the second part various questions connected to the first part are dealt with from the point of view, Conflict and Cooperation, suggested byJ. van Maanen to the participants of the Groningen conference.     

Further morphological and biochemical studies on normal and hybrid embryos of sea urchins

Zusammenfassung (1) Es wurde bei den SeeigelartenParacentrotus ,Arbacia undSphaerechinus sowie den drei BastardenPar ×Arb ,Arb ×Par undPar ×Sphaer für eine Reihe von Entwicklungsstadien die Anzahl der Kerne pro Keim bestimmt (Tabelle). Der morphogenetischen Hemmung der Bastarde entsprechen herabgesetzte Kernzahlen und parallel eine Herabsetzung der DNS-Synthese. (2) Es wurde bei den genannten reinen Arten und den Bastarden derUmsatz der RNS bestimmt. Er geht in allen Fällen, bei den reinen Arten wie bei den Bastarden, der DNS- Synthese parallel.

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Our work was supported by a grant from the Schweizerischer Nationalfonds zur Förderung der wissenschaftlichen Forschung. We express our sincere thanks to the Nationalfonds and also to the authorities at the Zoological Station at Naples for generous help and supply of materials and facilities. — This paper is thankfully dedicated byF. Baltzer toF. E. Lehmann for his kind hospitality in the Bernese Institute.     

The infinite and infinitesimal quantities of du Bois-Reymond and their reception

The mixed fortunes of Paul du Bois-Reymond's infinitary calculus and ideal boundary between convergence and divergence are traced from 1870 to 1914. Cantor, Dedekind, Peano, Russell, Pringsheim and others objected. Stolz, Borel, Hardy and others accepted, at least in part, and built further. Hausdorff to some extent effected a compromise. The differing attitudes of the different participants toward infinitesimals and infinitely large quantities are described. In addition to shedding some light on the status of infinites, the whole story serves as a study of mathematical change, and shows that the proof-refutation process described by Lakatos is only one aspect of mathematical development. The story also sheds some light on the rise of 20^th century functional analysis, algebra and topology.Wer je den grossen Bau der Welt bedacht und fühlte nicht, wie Gottes hoher Geist noch über den Gesetzen wacht und kreist-wie blind erscheint, wer Schöpfertum verlacht! Wir kennen kaum den kleinsten Teil davon: Gesetz ist Wunder, Zahl ist Weltenton. Albrecht Haushofer, Moabit Sonnets, 1944, LXIX, Kosmos     

“The True” in Gottlob Frege's “Über die Grundlagen der Geometrie”

In this essay, I examine the metaphysical and metalogical ramifications of Gottlob Frege's controversy with David Hilbert and Alwin Korselt, over Hilbert's Grundlagen der Geometrie. These ramifications include(1) Korselt's original appeals to general metatheoretic Deutungen (interpretations);(2) Hilbert's puzzling belief that whatever is consistent in some sense exists; and(3) Frege's semantic monist conviction that theoretical sense and reference (mathematical and other) must be eindeutig lösbar (uniquely solvable).My principal conclusions are(4) that Frege's position in (3) represented a pervasively dogmatic presumption that his newly discovered quantification theory must have a propositional metatheory (the True; the False); and(5) that this needless assumption adversely affected not only his polemic against the moderate semantic relativism of Hilbert and Korselt, but also his reception of type-theoretic ideas, and greatly facilitated his vulnerability to the sort of self-referential inconsistency Russell discovered in Grundgesetz V.These conclusions also seem to me to provide a conceptual framework for several of Frege's other arguments and reactions which might seem more particular and disparate. These include(6) his arbitrary restrictions on the range of second-order quantification, which undercut his own tentative attempts to give accounts of independence and semantic consequence;(7) his uncharacteristic hesitation, even dismay, at the prospect that such accounts might eventuate in a genuinely quantificational metamathematics, whose Gegenstände (objects) might themselves be Gedanken (thoughts); and, perhaps most revealingly(8) his otherwise quite enigmatic, quasi-stoic doctrine that genuine formal deduction must be from premises that are true.A deep reluctance to pluralize or iterate the transition from theory to meta-theory would also be consonant, of course, with Frege's vigorous insistence that there can be only one level each of linguistic Begriffe (concepts) and Gegenstände (objects). With hindsight, such an assumption may seem more gratuitous in the philosophy of language (where it contributed, I would argue, to Wittgenstein's famous transition to the mystical in 6.45 and 6.522 of the Tractatus); but its more implausible implications in this wider context seemed to emerge more slowly.In the mathematical test-case discussed here, however, such strains were immediately and painfully apparent; the first models of hyperbolic geometry were described some thirty years before Frege drafted his polemic against Hilbert's pioneering exposition. It is my hope that a careful study of Frege's lines of argument in this relatively straightforward mathematical controversy may suggest other, parallel approaches to the richer and more ambiguous problems of his philosophy of language.Niemand kann zwei Herren dienen. Man kann nicht der Wahrheit dienen und der Unwahrheit. Wenn die euklidische Geometrie wahr ist, so ist die nichteuklidische Geometrie falsch, und wenn die nichteuklidische wahr ist, so ist die euklidische Geometrie falsch.No one can serve two masters. One cannot serve truth and untruth. If Euclidean geometry is true, non-Euclidean geometry is false, and if non-Euclidean [geometry] is true, Euclidean geometry is false. Über Euklidische Geometrie [Frege 1969], p. 183.     

17β-Hydroxymethyl-steroide: Darstellung von 17α-Hydroxy-17β-hydroxymethyl-4-androsten-3-on aus Reichsteins Substanz S

Summary The synthesis of 17-hydroxy-17-hydroxymethyl-4-androsten-3-one fromReichsteins compound S is described. Transformation of 3,3-ethylenedioxy-17-hydroxy-17-hydroxymethyl-5-androsten into 17-methyl-isotestosterone demonstrates the configuration of the substituents at C-17.     

Il punto nella terminologia matematica greca

Summary In this note we claim that the two words and , which were used in Greece to indicate the geometrical point, had both been introduced in the scientific language in the first half of the IV^th century B.C., and that they became popular independently of each other in two different cultural circles, those of philosophy and of mathematics, respectively.We propose therefore, in contrast to a conjecture by Heiberg, a new explanation for the predominance of during the golden age of Greek mathematics and for the resurgence of during the period of decadence.

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Memoria presentata da A. Seidenberg     

Ein neues Verfahren zur Herstellung von 19-Norsteroiden

Summary The new methods for the production of 19-norsteroids described involve the conversion of 5-halogen-6-hydroxy-steroids into the corresponding 5-halogen-6:19-ethers either with lead tetraacetate or by the hypoiodite reaction^8,10. The 6:19-oxygen bridge is then opened reductively either directly or after oxidation of the 6:19-ethers to lactones or preferably after introduction of a ^4,6-3-oxo grouping. Acylolytic cleavage of the ⁴-3-oxo-6:19-ethers followed by alkaline hydrolysis gives ^4,6-3-oxo-19-hydroxy-steroids. The 19-hydroxycompounds formed are easily converted into 19-norsteroids by known methods.

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Über Steroide, 189. (vorläufige) Mitteilung; 188. Mitt. vgl.J. Kalvoda, J. Schmidlin, G. Anner undA. Wettstein, Exper.18, 398 (1962).     

Hoplonemertine worms—a new source of pyridine neurotoxins

Summary Two pyridine bases were isolated from the marine hoplonemertineAmphiporus angulatus (Fabricius) and identified by mass and PMR-spectroscopy as 2,3-bipyridyl and 3,2; 3,2; 4,3'-tetrapyridyl (Nemertelline). Nemertelline, the first tetrapyridyl natural product to be reported, shows a structural resemblance to the tobacco constituent nicotelline. The crustacean toxicity of 2,3-bipyridyl is very similar to that of nicotine, but its mammalian toxicity is negligible.We thank DoctorsN. Meinkoth andN. Riser for collecting specimens, Dr.F. Kuffner for providing the nicotelline sample, Dr.C. Westerman for recording initial PMR-spectra, and Dr.R. King for furnishing the computer simulation program and recording the high resolution mass spectra, and Mr.J. Babashak for use of the Kontes densitometer. This research was supported by an NIH-GRS grant and by the Veterans Administration (No. MRIS-9416).     

7α-hydroxylation of dehydroepiandrosterone in human testis and epididymis in vitro

Zusammenfassung Zerhackte menschliche Hoden und Epididymis wurden mit Dehydroepiandrosteron ohne Kofaktoren bebrütet und es wurden unter anderem 7-und 7-Hydroxydehydroepiandrosteron und 5-Androsten-3, 7, 17-triol charakterisiert. Die Ausbeute an 7-hydroxylierten Metaboliten war fast gleich in Hoden und Epididymis.

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The authors wish to thank Mr.J. Novák for his excellent technical assistance. We are indebted to Dr.J. E. Jirásek for generous performance of histological control of tissue and to Dr.S. Röhling for his kind pernission of radioactivity measurements.     

Pregnancy specificβ 1 — a product of the syncytiotrophoblast

Summary Pregnancy specific ₁ (PSG) has been identified in vitro in trophoblast cultures and in vivo, using transmission electron microscopy, in the syncytiotrophoblast, PSG may, like other pregnancy proteins, have immunosuppressive properties.This study was supported by a grant from the Medical Research Council. We thank Dr.D. R. Abramovich for making available the first trimester placentae and MissWanda Emslie for help in the tissue culture studies.     

The characteristic specificity of plasmocytoma lipids concerning their resistance to formdl-fractions with colloidal dextran

Zusammenfassung Papierelektrophoretische Lipiduntersuchungen von- und-Plasmacytom — Paraproteinseren nach Kolloidaldextranbelastung erfassen eine neue, in der Diagnostik des Plasmocytoms verwertbare Eigenschaft: die Paraproteinlipidkomponente (PL) vermag, entgegen den-Lipoproteinen, mit Dextran keine Assoziationsfraktion zu bilden.

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My thanks are due toJosipa Franjkovi for her technical assistance.     

On the structure of the natural dipeptide N-acetyl-aspartyl-glutamic acid (NAAGA)

Riassunto Si descrive la sintesi dei due dipeptidi isomeri acido N-acetil--l-aspartil-l-glutammico (I) e acido N-acetil--l-aspartil-l-glutammico (II). Il loro confronto con il NAAGA, dipeptide precedentemente isolato dal tessuto nervoso di alcuni mammiferi, ha dimostrato l'identità del nuovo metabolita con il-dipeptide (II).