Titlebook: L’Hôpital‘s Analyse des infiniments petits; An Annotated Transla Robert E Bradley,Salvatore J. Petrilli,C. Edward S Book 2015 Springer Inte

HEAVY

Use of the Differential Calculus for Finding the Greatest And the Least Ordinates, to Which Are Rednumbers of a function, l’Hôpital solves these problems by finding values of the abscissa . for which either . = 0 or . is infinite. Among the problems that l’Hôpital considers is finding the maximum ordinate on the closed loop of the Folium of Descartes, maximizing or minimizing surface area of soli

Cosmopolitan

Use of the Differential Calculus for Finding Inflection Points and Cusps,ts and cusps on a curve. In addition to the usual rectangular coordinates, l’Hôpital also considers the case where ordinates all emanate from a single point. Although these are not the polar coordinates that came into use in later centuries, because there is no accompanying angular coordinate, they

狗舍

Use of the Differential Calculus for Finding Evolutes,al when he tutored him in 1691–92. Chapter . is the first of six chapters that l’Hôpital had a more independent role in composing. It concerns finding the evolute of a given curve, which may be defined as the locus of the centers of curvature of that given curve. The study of these curves originated

Solace

Use of the Differential Calculus for Finding Caustics by Reflection,curves. In Chapter 6, l’Hôpital studies caustics by reflection, or catacaustics. This problem derives from optics and is essentially the study of envelopes made by light rays reflected in a mirror. L’Hôpital considers a variety of shapes of mirrors and of sources of light rays.

其他

Use of the Differential Calculus for Finding Caustics by Refraction,curves. In Chapter 7, l’Hôpital studies caustics by refraction, or dicaustics. This problem derives from optics and is essentially the study of envelopes made by light rays refracted through a lens. L’Hôpital considers a variety of shapes of lenses and sources of light rays.

Myosin

Use of the Differential Calculus for Finding the Points of Curved Lines That Touch An Infinity of Lcurves. In Chapter 8, l’Hôpital studies various envelopes that do not belong to the category of caustics by reflection or refraction. L’Hôpital considers envelopes of parabolas, of circles, and of various families of straight lines.

爱管闲事

The Solution of Several Problems That Depend upon the Previous Methods,in Chapters .–. This chapter begins with the celebrated theorem that now goes by the name L’Hôpital’s Rule. This rule is actually due to Bernoulli, and the version given here only covers the case in which . takes the indeterminate form . at a finite value of .. Much of the rest of the chapter is tak

弄皱

A New Method for Using the Differential Calculus with Geometric Curves, from Which We Deduce the Memay be investigated using the differential calculus. L’Hôpital demonstrates how all of these methods may be easily derived and justified using Leibniz’ differential calculus. Because Leibniz’ calculus can handle transcendental curves as well as algebraic curves, and does not require removing roots i

indenture

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