A treatise on surveying : containing the theory and practice : to which is prefixed a perspicuous system of plane trigonometry /

The above entries appear to constitute one work. cf. A treatise on surveying, p. 7.

A treatise on surveying : containing the theory and practice : to which is prefixed a perspicuous system of plane trigonometry : the whole clearly demonstrated and illustrated by a large number of appropriate examples, particularly adapted to the use of schools /

With: Mathematical tables / John Gummere. Stereotyped ed., carefully rev. and corrected. Philadelphia : Kimber & Sharpless, 1843.

A treatise on surveying, containing the theory and practice: to which is prefixed a perspicuous system of plane trigonometry.

Mode of access: Internet.

A treatise on plane and spherical trigonometry: with their most useful practical applications.

Title vignette.

Higher geometry and trigonometry : being the third part of a series on elementary and higher geometry, trigonomentary and mensuration : containing many valuable discoveries and improvements in mathematical science, especially in relation to the quadrature of the circle, and some other curves, as well as the cubature of certain curvilinear solids : designed as a text-book for collegiate and academic instruction, and as a practical compendium of mensuration /

With: Higher geometry and mensuration / by Nathan Scholfield.

Can partial coherence interferometry be used to determine retinal shape?

Purpose: To determine likely errors in estimating retinal shape using partial coherence interferometric instruments when no allowance is made for optical distortion. Method: Errors were estimated using Gullstrand’s No. 1 schematic eye and variants which included a 10 D axial myopic eye, an emmetropic eye with a gradient-index lens, and a 10.9 D accommodating eye with a gradient-index lens. Performance was simulated for two commercial instruments, the IOLMaster (Carl Zeiss Meditec) and the Lenstar LS 900 (Haag-Streit AG). The incident beam was directed towards either the centre of curvature of the anterior cornea (corneal-direction method) or the centre of the entrance pupil (pupil-direction method). Simple trigonometry was used with the corneal intercept and the incident beam angle to estimate retinal contour. Conics were fitted to the estimated contours. Results: The pupil-direction method gave estimates of retinal contour that were much too flat. The cornea-direction method gave similar results for IOLMaster and Lenstar approaches. The steepness of the retinal contour was slightly overestimated, the exact effects varying with the refractive error, gradient index and accommodation. Conclusion: These theoretical results suggest that, for field angles ≤30º, partial coherence interferometric instruments are of use in estimating retinal shape by the corneal-direction method with the assumptions of a regular retinal shape and no optical distortion. It may be possible to improve on these estimates out to larger field angles by using optical modeling to correct for distortion.

Is retinal shape different in Asians and Caucasians? Estimation from peripheral refraction and peripheral eye length methods

Purpose:Race appears to be associated with myopiogenesis, with East Asians showing high myopia prevalence. Considering structural variations in the eye, it is possible that retinal shapes are different between races. The purpose of this study was to quantify and compare retinal shapes between racial groups using peripheral refraction (PR) and peripheral eye lengths (PEL). Methods:A Shin-Nippon SRW5000 autorefractor and a Haag-Streit Lenstar LS900 biometer measured PR and PEL, respectively, along horizontal (H) and vertical (V) fields out to ±35° in 5° steps in 29 Caucasian (CA), 16 South Asian (SA) and 23 East Asian (EA) young adults (spherical equivalent range +0.75D to –5.00D in all groups). Retinal vertex curvature Rv and asphericity Q were determined from two methods: a) PR (Dunne): The Gullstrand-Emsley eye was modified according to participant’s intraocular lengths and anterior cornea curvature. Ray-tracing was performed at each angle through the stop, altering cornea asphericity until peripheral astigmatism matched experimental measurements. Retinal curvature and hence retinal co-ordinate intersection with the chief ray were altered until sagittal refraction matched its measurement. b) PEL: Ray-tracing was performed at each angle through the anterior corneal centre of curvature of the Gullstrand-Emsley eye. Ignoring lens refraction, retinal co-ordinates relative to the fovea were determined from PEL and trigonometry. From sets of retinal co-ordinates, conic retinal shapes were fitted in terms of Rv and Q. Repeated-measures ANOVA were conducted on Rv and Q, and post hoc t-tests with Bonferroni correction were used to compare races. Results:In all racial groups both methods showed greater Rv for the horizontal than for the vertical meridian and greater Rv for myopes than emmetropes. Rv was greater in EA than in CA (P=0.02), with Rv for SA being intermediate and not significantly different from CA and EA. The PEL method provided larger Rv than the PR method: PEL: EA vs CA 87±13 vs 83±11 m-1 (H), 79±13 vs 72±14 m-1 (V); PR: EA vs CA 79±10 vs 67±10 m-1 (H), 71±17 vs 66±12 m-1 (V). Q did not vary significantly with race. Conclusions:Estimates of Rv, but not of Q, varied significantly with race. The greater Rv found in EA than in CA and the comparatively high prevalence rate of myopia in many Asian countries may be related.

O ensino de trigonometria para deficientes visuais através do Multiplano Pedagógico

Este trabalho apresenta uma pesquisa sobre o ensino de Trigonometria para portadores de visão subnormal, desenvolvida com três jovens estudantes do 1 ano do Ensino Médio do Colégio Pedro II Unidade São Cristóvão - Rio de Janeiro, possuidores de diferentes tipos de deficiência visual. A intenção desta pesquisa é colaborar para uma verdadeira inclusão, onde estudantes normovisuais e deficientes visuais possam compartilhar o mesmo currículo e o mesmo ambiente de aprendizagem. Esta pesquisa traz algumas informações sobre as deficiências da visão e sobre o ensino da Trigonometria, além de apresentar o Multiplano Pedagógico, uma excelente ferramenta facilitadora da aprendizagem Matemática. Com o auxílio do Multiplano foram realizadas experiências com atividades direcionadas para o ensino de Matemática, em especial o conteúdo de Trigonometria, para esse público alvo, resgatando conteúdos inerentes ao bom acompanhamento do curso. Os jovens participantes da pesquisa participaram de forma ativa desde o direcionamento da ação até sua conclusão. Ela mostra que diversos conceitos podem ser melhor introduzidos quando auxiliados por materiais didáticos adaptados às necessidades dos educandos, porém ainda falta um bom caminho para que haja uma educação inclusiva de fato, com profissionais e escolas capacitados a atenderem de forma qualificada aos estudantes portadores de necessidades educacionais especiais.

Engineering school notebook which belonged to S.D. Woodruff

Engineering school notebook which belonged to S.D. Woodruff. This book contains logarithm notes, plane trigonometry, surveying and content of land. The outer page is torn and the notebook is quite discoloured. This does not affect the text. It has no covers, n.d.

University of Toronto exams

University of Toronto exams. These are in and envelope which is marked “Arts 1st year”. Included in this package are some text book pages [Latin] with the name Ham K. Woodruff written on them. The exams include: Anatomy, Arithmetic and Algebra, Medicine Chemistry, English, Euclid, French, Greek, Latin, Latin Grammar, Latin Prose (2 copies), Materia Medica and Therapeutics and Physiology for 1879. The exams for 1880 include Arithmetic and Algebra, Greek and Trigonometry. The 1881 Greek exam is also included. There is writing on some of the exams and some are worn and stained. The envelope is torn and stained and the textbook pages are slightly burned. This does not affect the text, 1879-1881.

MA167exam00pdf

Exam questions and solutions in PDF

MA167exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Exercise sheet 10

Exercises and solutions in LaTex

MA160exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA160exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files