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GALLEftY OF ILLUSTRIOUS ITALIAN WOMEN. 3...
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Note: This text has been automatically extracted via Optical Character Recognition (OCR) software. The text has not been manually corrected and should not be relied on to be an accurate representation of the item.
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Four Female Professors Of The University...
year , entitled Isiiiuzioni Analiiiche _? Milan , 1749 , two volumes in quarto .
The & st volume expounds all the operations of the analysis of iinite quantities . Next is developed the art of applying * these rules
to the solution of geometrical problems , determinate or indeterminate , _& £ the second and of superior degrees , rising in order from one to the
other ; the method for constructing their final equations , and for extracting the roots . The author then proceeds from the method of
maxima and minima to the method of tangents , the discovery of points of contrary flexure and of cusps . The analysis of infinitesimals
forms the subject of the second volume , in which are expounded the principles of the differential calculus , for the several orders of
infinitely small quantities , and the use of these principles is shewn in their application to the investigation of tangentsof maxima and
, mi ? iima , of points of contrary flexure and cusps , of evolutes , and of radii of curvature . 1
The integral calculus is next treated of , commencingwith the methods by means of which differential functions of the first order
of a single variable quantity are reduced to algebraical formulse or to quadratures of the circle or of the hyperbola . The principles of
the logarithmic calculus are given , the method of indeterminate coefficients is expounded , and the art of employing transformations in
order that the radical quantities may disappear . The use of series is shewn in order to find by approximation ,
the integrals of differential quantities of the same kind ; i . e . _^ composed of a single variable , when they are embarrassed by fractions
and radicals . After explaining * the rules , the art of applying them to the rectification of curves , the quadrature of the spaces they
enclose , to the cubature of solids , are successively dwelt upon . Passing * to the exponential calculus , the different ways are explained
by which it is possible to integrate differential functions , intermixed with _logarithmic quantities , or with quantities elevated to
variable powers : the manner of constructing the curves expressed by logarithmic and exponential equations , is given ; and the use and
application of this calculus is demonstrated by elegant solutions of various problems .
In the last part of this work , rules in the inverse method of tangents are explained , and those which lead to the integration
and to the construction of differential equations with two variable quantities . It is shewn by what means , and in what cases , it is
possible to arrive at the separation of variables . The use of this method is shewn in the solution of a number of problems , dependent
on the inverse method of tangents . The author then passes to the reduction of those equations which belong to a higher order .
The manner of reducing many general formulae , each one of which represents an infinity of these equations , is next treated of ; also the
methods employed by several geometricians , for reducing certain particular equations of the same kind , on which operation depends
vol . i . 2 d
Gallefty Of Illustrious Italian Women. 3...
_GALLEftY OF ILLUSTRIOUS ITALIAN WOMEN . 377


Citation

English Woman’s Journal (18581864), Aug. 1, 1858, page 377, in the NineteenthCentury Serials Edition (2008; 2018) ncse.ac.uk/periodicals/ewj/issues/ewj_01081858/page/17/
