Euklid's Data

Mode of access: Internet.

Evclidis Elementorvm libri XV. Accessit liber XVI. de solidorum regularium cuiuslibet intra quodlibet comparatione. Omnes perspicvis demonstrationibus, accuratísque scholiis illustrati: nunc quarto editi, ac multarum rerum accessione post primam editionem locupletati.

A different issue of the same year, with slight variations in printing.

A debate between Rev. A. Campbell and Rev. N.L. Rice, on the action, subject, design and administrator of Christian baptism : also, on the character of spiritual influence in conversion and sanctification, and on the expediency and tendency of ecclesiastic creeds, as terms of union and communion : held in Lexington, Ky., from the fifteenth of November to the second of December, 1843, a period of eighteen days /

Mode of access: Internet.

Elementi di geometria emendati, e restituiti al loro pristino stato dal V. Flauti.

1. Libri I-VI. degli Elemente. --2. XI--XIII. Elemente. Io. libro di Archimede sulla sfera, e sul cilindro; quello della misura del cerchio; e le note critiche, e geometriche.

Brevier legislative reports embracing short-hand sketches of the debates and journals of the General Assembly of the state of Indiana.

"Ariel & W.H. Drapier, Reporters."

Euclidis Elementa.

Lettered on cover: Bibliotheca scriptorum graecorum et romanorum Teubneriana. [S.g.]

Elements of geometry;

Mode of access: Internet.

Elements of geometry:

Mode of access: Internet.

Eukleidou stoicheia = Euclidis elementa : ex optimis libris in usum tironum : graece edita /

Errata slip inserted.

Christophori Clavii Bambergensis e Societate Iesv Opervm mathematicorvm tomvs primvs[-qvintvs]...

Vol. 1 contains In Euclidem commentarius only. The rest of v. 1 is bound at the end of v. 2. Refutatio Cyclometriae Iosephi Scaligeri is bound in v. 5.

The Role of Geometry in Wordsworth's "Science of Feelings"

Thesis (Ph.D.)--University of Washington, 2016-06

Diabetic retinopathy and blockade of the renin–angiotensin system:new data from the DIRECT study programme

The pathogenesis and medical management of diabetic retinopathy is reviewed. The importance of good control of blood glucose and blood pressure remain key elements in the prevention and treatment of diabetic retinopathy, and a number of specific metabolic pathways have been identified that may be useful additional targets for therapeutic intervention. Trial data, however, aimed specifically to answer the questions of optimum medical management are limited, so the DIRECT study of renin-angiotensin blockade using oral candesartan 32 mg daily is a welcome addition to our knowledge. This arose from the promising improvement of retinopathy outcomes in the EUCLID study of lisinopril in type I diabetes. In DIRECT, 5 years of candesartan treatment in type I diabetes reduced the incidence of retinopathy by two or more steps (EDTRS) in severity by 18% (P = 0.0508) and, in a post hoc analysis, reduced the incidence of retinopathy by three-step progression by 35% (P = 0.034). In type I diabetes patients there was no effect on progression of established retinopathy. In contrast, in type II diabetes, 5 years of candesartan treatment resulted in 34% regression of retinopathy (P ≤0.009). Importantly, an overall significant change towards less-severe retinopathy was noted in both type I and II diabetes (P0.03). Although there is still no absolute proof that these effects were specific to RAS blockade, or just an effect of lower blood pressure, it is reasonable to conclude that candesartan has earned a place in the medical management of diabetic retinopathy, to prevent the problem in type I diabetes and to treat the early stages in type II diabetes. © 2010 Macmillan Publishers Limited All rights reserved.

Proposta de ensino de geometria euclidiana plana para o sexto ano do ensino fundamental sob a ótica do raciocínio lógico-dedutivo

This study will introduce a brief history of the Geometry development, focused in the appearing of the organization in the logical deductive structure achieved by Euclid. Following will be discussed the situation of the learning and teaching of geometry topics since antiquity until the present day, where we will notice that it does not happen with the logical-deductive perspective. After this contextualization, we will propose the realization of a geometry workshop for students of the sixth grade of elementary school, focusing to the development of logical-deductive reasoning. Applied to workshop, changes were observed in the organization of thought of the participating students in the research, furthering the understanding of the concepts and properties of flat euclidean geometry.

Visual Insight in Geometry

According to a traditional rationalist proposal, it is possible to attain knowledge of certain necessary truths by means of insight—an epistemic mental act that combines the 'presentational' character of perception with the a priori status usually reserved for discursive reasoning. In this dissertation, I defend the insight proposal in relation to a specific subject matter: elementary Euclidean plane geometry, as set out in Book I of Euclid's Elements. In particular, I argue that visualizations and visual experiences of diagrams allow human subjects to grasp truths of geometry by means of visual insight. In the first two chapters, I provide an initial defense of the geometrical insight proposal, drawing on a novel interpretation of Plato's Meno to motivate the view and to reply to some objections. In the remaining three chapters, I provide an account of the psychological underpinnings of geometrical insight, a task that requires considering the psychology of visual imagery alongside the details of Euclid's geometrical system. One important challenge is to explain how basic features of human visual representations can serve to ground our intuitive grasp of Euclid's postulates and other initial assumptions. A second challenge is to explain how we are able to grasp general theorems by considering diagrams that depict only special cases. I argue that both of these challenges can be met by an account that regards geometrical insight as based in visual experiences involving the combined deployment of two varieties of 'dynamic' visual imagery: one that allows the subject to visually rehearse spatial transformations of a figure's parts, and another that allows the subject to entertain alternative ways of structurally integrating the figure as a whole. It is the interplay between these two forms of dynamic imagery that enables a visual experience of a diagram, suitably animated in visual imagination, to justify belief in the propositions of Euclid’s geometry. The upshot is a novel dynamic imagery account that explains how intuitive knowledge of elementary Euclidean plane geometry can be understood as grounded in visual insight.