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This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, plane and spherical trigonometry, and mensuration. [This book was translated by David Brewster. It was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, plane and spherical trigonometry, and mensuration. [This book was translated by David Brewster. It was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, the proportions of figures and the measurement of areas, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, spherical triangles and spherical polygons, regular polyhedrons, plane and spherical trigonometry, and mensuration. [This book was translated by David Brewster. It was revised and adapted by Charles Davies.]

This textbook covers geometry and trigonometry and presents problems for student consideration. Contents include geometry, plane trigonometry, analytical trigonometry, spherical trigonometry, and mensuration. [This book was adapted by Charles Davies.]

The polymerase chain reaction (PCR) for amplification of DNA has become a very useful tool in scientific research and analytical laboratories, yet conventional techniques are time-consuming, and the reagents are expensive. Miniaturization of this technique has the potential to drastically reduce amplification time and reagent consumption while simultaneously improving the efficiency of the reaction. Increasing the surface area-to-volume ratio using microfluidic reaction chambers allows homogeneous solution temperatures to be achieved much more rapidly than in conventional heating blocks. Employing infrared radiation to selectively heat the reaction solution can additionally reduce the time and energy needed for thermocycling; the reaction container is not heated and can even serve as a heat sink for enhancement of cooling. Microchip systems also provide the potential for fabrication of structures for additional processing steps directly in line with the PCR chamber. Not only can amplification be integrated with product separation and analysis, but sample preparation steps can also be incorporated prior to amplification. The ultimate goal is a miniature total-analysis-system with seamlessly coupled sample-in/answer-out capabilities that consumes very low volumes of reagents and drastically reduces the time for analysis. This chapter will focus on the materials and methods involved in simple straight-channel microchip PCR on glass substrates using non-contact thermocycling. [ABSTRACT FROM AUTHOR]

We discuss two sets of non-trivial effects affecting the motion of high-Reynolds number gas bubbles rising in still liquid which have been significantly clarified thanks to direct numerical simulations making use of a suitable boundary-fitted technique.We first summarize some features of the interaction between two spherical bubbles rising side by side in a viscous liquid. Then we briefly discuss some aspects of the path instability of a spheroidal bubble rising in a low-viscosity liquid. [ABSTRACT FROM AUTHOR]

Plants possess a range of tools for combating a Botrytis infection. This chapter will describe three types of pre-formed and induced plant defence compounds and discuss their effectiveness in restricting Botrytis infection. Case studies are presented on several types of secondary metabolites: stilbenes including resveratrol, saponins including ??-tomatin, cucurbitacins, proanthocyanidins and tulipalin A. Evidence is presented suggesting that Botrytis species have evolved mechanisms to counteract some of these defence responses. Secondly, we discuss the role of structural barriers and cell wall modification in preventing penetration. Finally the contribution of PR proteins to resistance is discussed. [ABSTRACT FROM AUTHOR]