A Short View of the First Principles of Differential CalculusJ. Deighton, 1824 - 198 strán (strany) |
Vyhľadávanie v obsahu knihy
Výsledky 1 - 5 z 13.
Strana ii
... sufficiently established by experiment and observation , it enables us , by a series of legitimate inferences , to arrive at the knowledge of other truths , so vast in their nature , that we might well have imagined them to lie beyond ...
... sufficiently established by experiment and observation , it enables us , by a series of legitimate inferences , to arrive at the knowledge of other truths , so vast in their nature , that we might well have imagined them to lie beyond ...
Strana xxii
... sufficiently so , for all the purposes of calculation . Since , then , the doctrine of 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 ...
... sufficiently so , for all the purposes of calculation . Since , then , the doctrine of 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 ...
Strana 21
... sufficiently small , the series CxDxFx3 + & c . would have been rendered less than ( B ) , and con- sequently Cx2 + Dx3 + Fx1 + & c . the remaining part of the series would then become less than the term Bx . COR . Hence it appears ...
... sufficiently small , the series CxDxFx3 + & c . would have been rendered less than ( B ) , and con- sequently Cx2 + Dx3 + Fx1 + & c . the remaining part of the series would then become less than the term Bx . COR . Hence it appears ...
Strana 121
... sufficiently diminished ; hence , Rn is greater than Qn , and , therefore , the curve lies below the tangent . In the same manner it may be shown , that if f ( x ) be positive , the curve lies above the tangent . Ex . 1. Suppose the ...
... sufficiently diminished ; hence , Rn is greater than Qn , and , therefore , the curve lies below the tangent . In the same manner it may be shown , that if f ( x ) be positive , the curve lies above the tangent . Ex . 1. Suppose the ...
Strana 123
... sufficiently small , we shall have one of the quantities f ( x + h ) , and f2 . ( x - h ) positive , and the other negative ; and , consequently , the curve on one side of this point is convex , and on the other side concave ; hence ...
... sufficiently small , we shall have one of the quantities f ( x + h ) , and f2 . ( x - h ) positive , and the other negative ; and , consequently , the curve on one side of this point is convex , and on the other side concave ; hence ...
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.