Book details

The Geometry of Rene Descartes (Dover Books on Mathematics) (Paperback)(English / French / Latin)
$9.30  Save $9.53 50% off  RRP $18.83 Free delivery worldwide Available
Dispatched in 3 business days When will my order arrive?   Also available in...
 Hardback $32.11
DescriptionThe great work that founded analytical geometry. Included here is the original French text, Descartes' own diagrams, together with the definitive SmithLatham translation. "The greatest single step ever made in the progress of the exact sciences."  John Stuart Mill.
 Publisher: Dover Publications Inc.
 Published: 07 August 1999
 Format: Paperback 244 pages
 See: Full bibliographic data
 Categories: Geometry  Analytic Geometry  Topology  History Of Mathematics
 ISBN 13: 9780486600680 ISBN 10: 0486600688
 Sales rank: 225,493
Other books
Showing items 1
to
10
of
10
Full bibliographic data for The Geometry of Rene Descartes
 Title
 The Geometry of Rene Descartes
 Authors and contributors
 Physical properties
 Format: Paperback
Number of pages: 244
Width: 137 mm
Height: 198 mm
Thickness: 15 mm
Weight: 249 g  Language
 English
French
Latin  ISBN
 ISBN 13: 9780486600680
ISBN 10: 0486600688  Classifications
BIC E4L: MAT
Nielsen BookScan Product Class 3: S7.8
B&T Book Type: NF
DC22: 516
DC21: 516
Ingram Subject Code: SE
Libri: ISE
B&T Merchandise Category: SCI
B&T General Subject: 710
BIC subject category V2: PBM
LC classification: QA
LC subject heading: ,
Abridged Dewey: 516
BIC subject category V2: PBP
WarengruppenSystematik des deutschen Buchhandels: 26260
BISAC V2.8: MAT012000, MAT015000, MAT012020
Thema V1.0: PBP, PBM
 Publisher
 Dover Publications Inc.
 Imprint name
 Dover Publications Inc.
 Publication date
 07 August 1999
 Publication City/Country
 New York
 Table of contents
 BOOK I PROBLEMS THE CONSTRUCTION OF WHICH REQUIRES ONLY STRAIGHT LINES AND CIRCLES How the calculations of arithmetic are related to the operations of geometry "How the multiplication, division, and the extraction of square root are performed geometrically" How we use arithmetic symbols in geometry How we use equations in solving problems Plane problems and their solution Example from Pappus Solution of the problem of Pappus How we should choose the terms in arriving at the equation in this case How we find that this problem is plane when not more than five lines are given BOOK II ON THE NATURE OF CURVED LINES What curved lines are admitted in geometry "The method of distinguishing all curved lines of certain classes, and of knowing the ratios connecting their points on certain straight lines" There follows the explanation of the problem of Pappus mentioned in the preceding book Solution of this problem for the case of only three or four lines Demonstration of this solution Plane and solid loci and the method of finding them The first and simplest of all the curves needed in solving the ancient problem for the case of five lines Geometric curves that can be described by finding a number of their points Those which can be described with a string "To find the properties of curves it is necessary to know the relation of their points to points on certain straight lines, and the method of drawing other lines which cut them in all these points at right angles" General method for finding straight lines which cut given curves and make right angles with them Example of this operation in the case of an ellipse and of a parabola of the second class Another example in the case of an oval of the second class Example of the construction of this problem in the case of the conchoid Explanation of four new classes of ovals which enter into optics The properties of these ovals relating to reflection and refraction Demonstration of these properties "How it is possible to make a lens as convex or concave as we wish, in one of its surfaces, which shall cause to converge in a given point all the rays which proceed from another given point" How it is possible to make a lens which operates like the preceeding and such that the convexity of one of its surfaces shall have a given ratio to the convexity or concavity of the other "How it is possible to apply what has been said here concerning curved lines described on a plane surface to those which are described in a space of three dimensions, or on a curved surface" BOOK III ON THE CONSTRUCTION OF SOLID OR SUPERSOLID PROBLEMS On those curves which can be used in the construction of every problem Example relating to the finding of several mean proportionals On the nature of equations How many roots each equation can have What are false roots How it is possible to lower the degree of an equation when one of the roots is known How to determine if any given quantity is a root How many true roots an equation may have "How the false roots may become true, and the true roots false" How to increase or decrease the roots of an equation "That by increasing the true roots we decrease the false ones, and vice versa" How to remove the second term of an equation How to make the false roots true without making the true ones false How to fill all the places of an equation How to multiply or divide the roots of an equation How to eliminate the fractions in an equation How to make the known quantity of any term of an equation equal to any given quantity That both the true and the false roots may be real or imaginary The reduction of the cubic equations when the problem is plane The method of dividing an equation by a binomial which contains a root Problems which are solid when the equation is cubic The reduction of equations of the fourth degree when the problem is plane Solid problems Example showing the use of these reductions General rule for reducing equations about the fourth degree General method for constructing all solid problems which reduce to an equation of the third or the fourth degree The finding of two mean proportionals The trisection of an angle That all solid problems can be reduced to these two constructions The method of expressing all the roots of cubic equations and hence of all equations extending to the fourth degree "Why solid problems cannot be constructed without conic sections, nor those problems which are more complex without other lines that are also more complex" General method for constructing all problems which require equations of degree not higher than the sixth The finding of four mean proportionals