A Short View of the First Principles of Differential CalculusJ. Deighton, 1824 - 198 strán (strany) |
Vyhľadávanie v obsahu knihy
Výsledky 1 - 5 z 7.
Strana iii
... limits of our mental faculties , yet , it must still be remembered , * These , I imagine , are the kind of problems , which Eubulus stigmatizes as being mere puzzles . To this class belongs the integration of many differentials and ...
... limits of our mental faculties , yet , it must still be remembered , * These , I imagine , are the kind of problems , which Eubulus stigmatizes as being mere puzzles . To this class belongs the integration of many differentials and ...
Strana xxi
... limits , as in most treatises on the Differential Calculus , but have endeavoured to give a rigid de- monstration of every proposition . The reason why Newton introduced his method of prime and ultimate ratios into Geometry , is ...
... limits , as in most treatises on the Differential Calculus , but have endeavoured to give a rigid de- monstration of every proposition . The reason why Newton introduced his method of prime and ultimate ratios into Geometry , is ...
Strana xxii
... limits is in its very nature so liable to be misunderstood , I cannot but hope , that the following Treatise will not be found entirely useless . Since my only object in composing it , was , to explain the reasoning , upon which the ...
... limits is in its very nature so liable to be misunderstood , I cannot but hope , that the following Treatise will not be found entirely useless . Since my only object in composing it , was , to explain the reasoning , upon which the ...
Strana 4
... limit to the number of parts into which a linear unit can be divided , there can also be no limit to the degree of accuracy , with which incommensurable lines may be represented by numbers * . * That lines , admitting no common measure ...
... limit to the number of parts into which a linear unit can be divided , there can also be no limit to the degree of accuracy , with which incommensurable lines may be represented by numbers * . * That lines , admitting no common measure ...
Strana 7
... limit of S ' ; and , consequently , Aa is the limit of S'a . Since , then , both P and Aa are equal to the quantity , to which S'a approximates as its limits , when ( 2 ) is indefinitely increased , P must = Aa ; and , therefore , 4 P ...
... limit of S ' ; and , consequently , Aa is the limit of S'a . Since , then , both P and Aa are equal to the quantity , to which S'a approximates as its limits , when ( 2 ) is indefinitely increased , P must = Aa ; and , therefore , 4 P ...
Časté výrazy a frázy
1+p² A'PQ a²+x² abscissa algebraic algebraic curve Analytics angle LSP arc PQ assume axes calculated cient circle A"PQ circle of curvature circle Pq co-ordinates coeffi common logarithm consequently considered contrary flexure convex curve APQ cylinder d²p dp dp dp² dx² Dx³ equal equation finite function ƒ² ƒ³ given line greater than SQ Hence horizontal axis hyp.log initial line length less lies linear unit logarithmic spiral manifest Mathematics maximum minimum negative ordinate parabola parallelopiped perpendicular point of contrary positive Prop proposition R₂ radius of curvature radius vector rect rectangle represented second differential coefficient series D spiral is concave straight line substituted suppose tangent Taylor's theorem
Populárne pasáže
Strana xvii - Excudent alii spirantia mollius aera, Credo equidem, vivos ducent de marmore vultus, Orabunt causas melius, caelique meatus Describent radio et surgentia sidera dicent; Tu regere imperio populos, Romane, memento : Hae tibi erunt artes, pacisque imponere morem, Parcere subiectis, et debellare superbos.
Strana xvii - Excudent alii spirantia mollius aera, credo equidem, vivos ducent de marmore vultus, orabunt causas melius, caelique meatus describent radio et surgentia sidera dicent : 850 tu regere imperio populos, Romane, memento (hae tibi erunt artes), pacisque imponere morem, parcere subiectis et debellare superbos.
Strana 50 - The differential of the product of any number of functions is equal to the sum of the products which arise by multiplying the differential of each function by the product of all the others: d(uts) = tsdu + usdt -4- utds.
Strana 5 - The area of a rectangle is equal to the product of the length by the breadth.
Strana 44 - It was also shown in the same article, that the differential of the sum of any number of functions is equal to the sum of their...
Strana 67 - Show how to divide a straight line into two parts so that the sum of the squares on the parts shall be equal to the square on a given line.
Strana 74 - The sum of the logarithms of two numbers, is the logarithm of the product of those numbers; and the difference of the logarithms of two numbers, is the logarithm of the quotient of one of the numbers divided by the other. (Art. 2.) In Briggs' system, the logarithm of 10 is 1.
Strana 133 - ... the angle which the tangent to the curve at that point makes with the axis of strain ; I will call this angle <f>.
Strana 1 - If two sides and the included angle of a triangle are given, show how to solve the triangle. Ex. The two sides are 345, 174 feet respectively, and the included angle is 37° 20'; find the remaining angles of the triangle. log.,» 5'19 = -715167, log. tan. 71° 20/ = 10-471298. log.,0 1-71 = -232996, log. tan. 44° 17
Strana 24 - If three magnitudes of the same kind are so related that the first is greater than the second, and the second greater than the third, then the first is greater than the third.