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.

Proposal for a Trigonometric Method to Evaluate the Abduction Angle of the Lower Limbs in Neonates

It is difficult to precisely measure articular arc movement in newborns using a goniometer. This article proposes an objective method based on trigonometry for the evaluation of lower limb abduction. With the newborn aligned in the dorsal decubitus position, 2 points are marked at the level of the medial malleolus, one on the sagittal line and the other at the end of the abduction. Using the right-sided line between these 2 points and a line from the medial malleolus to the reference point at the anterior superior iliac spine or umbilical scar, an isosceles triangle is drawn, and half of the inferential abduction angle is obtained by calculating the sine. Twenty healthy full-term newborns comprise the study cohort. Intersubject and intrasubject variability among the abduction angle values (mean [SD], 37 degrees [4]degrees) is low. This method is advantageous because the measurement is precise and because the sine can be used without approximation.

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

Engenheiros portugueses no século XVIII: as suas "geometrias especulativas"

O século XVIII Português foi, à semelhança do resto da Europa, fértil em alterações académicas, científicas e ideológicas. O desenvolvimento da ciência e da técnica, o surgimento das primeiras máquinas, impulsionou a área do saber, que atualmente chamamos de engenharia. Em Portugal (à época ainda um império do qual fazia parte, entre outros, o Brasil), as escolas técnicas e militares consolidam-se e surgem vários engenheiros e militares de renome cujas obras se difundem pelo reino. Manuel de Azevedo Fortes (1660-1749), engenheiro-mor do reino Português, publicou, em 1728 e 1729, os dois tomos de uma das suas obras maiores, O Engenheiro Português, obra dedicada à formação dos engenheiros na Academia Militar de Lisboa.. A primeira parte deste tratado aborda os conhecimentos matemáticos que Azevedo Fortes considera essenciais na formação dos engenheiros. Na sua Geometria Especulativa, um manuscrito datado de 1724, aborda os elementos de geometria e trigonometria, sem esquecer as suas aplicações. O Brigadeiro José Fernandes Pinto Alpoim (1700-1765), engenheiro que se destacou na arquitetura e fortificação do Brasil no século XVIII, publicou o Exame de Artilheiros em 1744 e Exame de Bombeiros em 1748, obras contendo os princípios da geometria e da trigonometria e as suas aplicações à engenharia militar que se destinavam ao ensino dos militares na Academia Militar do Rio de Janeiro, onde era professor. Nesta comunicação analisaremos a matemática, em particular a geometria, presente nestas obras, salientando não só os conteúdos abordados mas a ênfase dada às aplicações desses conteúdos nos contextos militares da época.

Método alternativo a la modelización gráfica en el cálculo del espacio necesario para crear zonas lineales de aparcamiento en vías urbanas

Aquest mètode permet calcular numèricament l¿espai necessari per crear zones lineals d¿aparcament d¿ n places sense haver de recórrer a la modelització gràfica. Està dissenyat especialment per trobar amb facilitat les característiques òptimes de zones d¿aparcament en vies amb limitacions d¿espai. Aquest estudi és una anàlisi trigonomètrica d¿una àrea d¿aparcament tenint en compte el comportament d¿un vehicle estàndard en la maniobra d¿estacionament.

Mètode alternatiu a la modelització gràfica en el càlcul de l'espai necessari per crear zones lineals d'aparcament en vies urbanes

Aquest mètode permet calcular numèricament l'espai necessari per crear zones lineals d'aparcament d' n places sense haver de recórrer a la modelització gràfica. Està dissenyat especialment per trobar amb facilitat les característiques òptimes de zones d'aparcament en vies amb limitacions d'espai. Aquest estudi és una anàlisi trigonomètrica d'una àrea d'aparcament tenint en compte el comportament d'un vehicle estàndard en la maniobra d'estacionament.

Lasikuituputkien kelauslinjan automatisointi

Lasikuituputkien kelaamiseen tarkoitettu automaatio voidaan toteuttaa suorakulmaisen kolmion trigonometrian perusteella. Kelaaminen tapahtuu pyörittämällä muottia ja liikuttamalla samalla muottia sivuttain. Näin tehdessä saadaan kelattavat lasikuitulangat leviämään koko muotin leveydelle. Jos langat halutaan saada kelattua tiiviisti toistensa viereen, on muotin liikuttava tietty matka yhtä muotin pyörähdystä kohden. Matkaa kutsutaan nousuksi. Nousu riippuu lankojen muodostaman kimpun leveydestä, kelauskulmasta ja muotin säteestä. Kelauskulmalla voidaan vaikuttaa kelattavan tuotteen aksiaaliseen ja pitkittäiseen lujuuteen. Kelauskoneen automaatiojärjestelmä koostuu sähkökäytöistä, ohjaavasta yksiköstä, valvomosta ja erilaisista antureista. Eri osat yhdistetään toisiinsa väylätekniikalla. Sähkökäytöt ovat yleensä servokäyttöjä, koska niiltä vaaditaan tarkkuutta ja nopeutta. Ohjaavana yksikkönä toimii yleensä teollisuus logiikka. Anturointia tarvitaan esimerkiksi hartsin lämpötilan säätöön ja lankojen ratakireyden säätöön. Anturoinnilla ja säädöillä pyritään parantamaan kelattavan tuotteen laatua. Koneen ohjelmallinen toteutus vaatii kelauskoneen mekaniikan ja kelausprosessin ymmärtämistä. Lisäksi on huomioitava koneen käyttäjät ja heidän turvallisuus.

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