In the late sixteenth century a number of mathematicians tried to introduce geometrical methods into surveying practice, to be based on simplified astronomical instruments, angle measurement, and triangulation. A measure of success is indicated by the acceptance of the simple theodolite, but the surveyors resisted such complex instruments as the altazimuth theodolite, recipiangle, and trigonometer. Counter-proposals, in particular the plane table, threatened to undermine the geometrical programme, but by the mid-seventeenth century a stable compromise had evolved. Among other things, the (...) demise of the shadow square indicates that angle measurement was then part of surveying practice. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The classical Feferman–Vaught Theorem for First Order Logic explains how to compute the truth value of a first order sentence in a generalized product of first order structures by reducing this computation to the computation of truth values of other first order sentences in the factors and evaluation of a monadic second order sentence in the index structure. This technique was later extended by Läuchli, Shelah and Gurevich to monadic second order logic. The technique has wide applications in decidability and (...) definability theory. Here we give a unified presentation, including some new results, of how to use the Feferman–Vaught Theorem, and some new variations thereof, algorithmically in the case of Monadic Second Order Logic MSOL . We then extend the technique to graph polynomials where the range of the summation of the monomials is definable in MSOL . Here the Feferman–Vaught Theorem for these polynomials generalizes well known splitting theorems for graph polynomials. Again, these can be used algorithmically. Finally, we discuss extensions of MSOL for which the Feferman–Vaught Theorem holds as well. (shrink)

We investigate the expressive power of second-order logic over finite structures, when two limitations are imposed. Let SAA ) be the set of second-order formulas such that the arity of the relation variables is bounded by k and the number of alternations of second-order quantification is bounded by n . We show that this imposes a proper hierarchy on second-order logic, i.e. for every k , n there are problems not definable in AA but definable in AA for some c (...) 1 , d 1 . The method to show this is to introduce the set AUTOSAT of formulas in F which satisfy themselves. We study the complexity of this set for various fragments of second-order loeic. For first-order logic FOL with unbounded alternation of quantifiers AUTOSAT is PSpace complete. For first-order logic FOL n with alternation of quantifiers bounded by n , AUTOSAT is definable in AA . AUTOSAT) is definable in AA for some c 1 , d 1. (shrink)

The essays collected together in this volume, many of them written by leading scholars in the field, explore the commonsensical fact that our presence as..

A dictionary definition of Bioethics is, 'the ethics, or moral principles and rules of conduct, of medical and biological research'. This book is an introductory text of just biological and not medical bioethics. It covers the ethics of experimentation, including genetic manipulation, in plants and animals; ethics and biodiversity, ethics and the environment. There is increasing interest in bioethics - both in academia and by the media and the general public. Awareness of bioethics is incorporated into Biological / Environmental Science (...) courses, plus the first dedicated modular courses on bioethics are starting up. * Includes case studies * Has questions for students * Chapters include environmental, animal, agricultural and reproductive ethics as well as a wide range of issues regarding genetic manipulation. (shrink)

A dictionary definition of Bioethics is, 'the ethics, or moral principles and rules of conduct, of medical and biological research'. This book is an introductory text of just biological and not medical bioethics. It covers the ethics of experimentation, including genetic manipulation, in plants and animals; ethics and biodiversity, ethics and the environment. There is increasing interest in bioethics - both in academia and by the media and the general public. Awareness of bioethics is incorporated into Biological / Environmental Science (...) courses, plus the first dedicated modular courses on bioethics are starting up. Includes case studies Has questions for students Chapters include environmental, animal, agricultural and reproductive ethics as well as a wide range of issues regarding genetic manipulation. (shrink)

Chapter 47 contains a sentence which has been the subject of a good deal of controversy and is manifestly corrupt. In the codex it reads as follows: κα τοᾁτων πνω μαιμᾃτατον θνος Bακτριανν π βασιλα οσαν διον τπον κα 'Aλξανδρος ρμηθες π τν μερν τοᾁτων ρι τοȗ Γγγον διλθε κτλ. Attempts have been made to connect this sentence with the rulers of the Kushan dynasty. It has even been suggested that οσαν represents Kονσαν : the suggestion naturally won no acceptance, (...) but one may point out that in any case it failed to attack the real difficulty, which lies in the words διον τπον On that essential point, the views of recent editors have both varied and combined. (shrink)

κάτοπτρον, which is in all the manuscripts, was emended by Canter to κάτοπτον, and this emendation, or Headlam's κατόπτην, has been received by subsequent editors. Those who read κάτοπτον have been in the habit of taking the word to mean here ‘looking down upon’, and in support of this interpretation they sometimes adduce a scholium in M, κατόψιον. This does seem to prove that the scholar, whose note is copied in our scholium, found κάτοπτον in his text. Presumably he took (...) Σαρωνικο πορθμο κάτοπτον to signify ‘descried from the Saronic gulf’, having very possibly in his mind the phrase in Euripides, Hippolytus 30, where the temple of Cypris is said to be κατόψιον γς τσδε, visible from Troezen. At least we ought not without proof to lay to his account what appears to be the solecism of regarding κάτοπτον as if it meant ‘looking down upon’. Headlam's κατόπτην has at least an active force, but I cannot find that it means ‘one who looks down upon’, if that is the sense desired; it is a ‘spy’ or an ‘inspector’. And, at the end of all discussion, when one asks what in fact is this peak or headland that ‘looks down upon the Saronic crossing’, then commentators take refuge in silence or tend to contradict one another. An emendation that nobody can be sure he understands can hardly be regarded as satisfactory. It may be feared that what has happened is this. In order to get rid of κάτοπτρον, which appeared to them devoid of meaning, editors have introduced into the text a word which does not mean what they want it to mean, and which, if it had that meaning, would still present us with a picture which no man can recognize. (shrink)

Observations with respect to the relationship between symptoms and diseases can seriously be biased by selection phenomena. This selection may occur from the general population, via consultation behavior, diagnostic and therapeutic activities of the general practitioner, and by referral.Relationships may be suggested and reproduced even if they do not exist in unselected populations, as a product of diagnostic routines. Correction for selection bias can only be achieved by choosing proper comparison groups. While this can be done in a general practice (...) setting, this is almost impossible after referral, as is demonstrated in this paper. Surprisingly, the most unbiased estimation of the relationship between symptoms and diseases after referral can be made from patient groups that are referred for reason unrelated to the disease under study. (shrink)

As is well known, this poem, which stood in the Anthologia Latina, is preserved in two MSS. only, the Salmasian and the Pithoean , Nos. 10318 and 8071 in the Bibliothèque Nationale in Paris; ‘the handwriting dates’ the former ‘as written at the end of the seventh or the beginning of the eighth century; the other…is about two hundred years later in date. Modern scholars regard both MSS. as traceable to a common archetype, probably of the sixth century’ . At (...) first sight these MSS. seem quite untrust-worthy, for they differ from each other in more than one hundred words, while the scribe of S copied the refrain incorrectly twice, the scribe of T twice as often. Strangely enough, however, these variations are comparatively unimportant, for most of them disappear when the spelling of the two clerks is assimilated to some recognized usage. Each manuscript in turn corrects the other in many of these passages, and conjecture has successfully emended nearly all of the remainder—the variation S peruiclanda, T peruigila in v. 47 is perhaps the only passage of this kind which still causes anxiety. The grave corruptions of the text are found in passages in which the MSS. are in agreement; they agree exactly in five lacunae, T having an additional one; in two or more misplaced passages; in the placing of the refrain, with all of which matters I deal below; they agree exactly in an error in the title ‘Peruirgilium’ for ‘Peruigilium,’ and in about twelve lines, of which vv. 51 and 79 have almost certainly been preserved in an incorrect form. (shrink)

For the sentences of languages that contain operators that express the concepts of definiteness and indefiniteness, there is an unavoidable tension between a truth-theoretic semantics that delivers truth conditions for those sentences that capture their propositional contents and any model-theoretic semantics that has a story to tell about how indetifiniteness in a constituent affects the semantic value of sentences which imbed it. But semantic theories of both kinds play essential roles, so the tension needs to be resolved. I argue that (...) it is the truth theory which correctly characterises the notion of truth, per se. When we take into account the considerations required to bring model theory into harmony with truth theory, those considerations undermine the arguments standardly used to motivate supervaluational model theories designed to validate classical logic. But those considerations also show that celebration would be premature for advocates of the most frequently encountered rival approach - many-valued model theory. (shrink)

This Routledge Revival sees the reissue of a seminal work by British economist, sociologist and academic John A. Hobson, elucidating his views on a variety of topics across the social sciences. He makes particular reference to the struggle between the disinterested urge of the social scientist and the interests and other motive forces which tend to influence and mould his processes of inquiry. The work is split into three parts, focussing upon free-thinking, economics and political ethics respectively.