A Short View of the First Principles of Differential CalculusJ. Deighton, 1824 - 198 strán (strany) |
Vyhľadávanie v obsahu knihy
Výsledky 1 - 5 z 30.
Strana 8
... assumed of any magnitude ; hence , P and Aa , are not unequal ; hence , 4P = 4Aa , or the numerical value of the content of the cylinder From the preceding propositions , we may easily find the areas of most rectilinear figures . Thus ...
... assumed of any magnitude ; hence , P and Aa , are not unequal ; hence , 4P = 4Aa , or the numerical value of the content of the cylinder From the preceding propositions , we may easily find the areas of most rectilinear figures . Thus ...
Strana 11
... assumed equal to some number in the series 4 , 8 , 16 , & c . , which is greater than π 3 which is absurd . Therefore P is not greater than Ca , and in the same manner it may be shown not to be less ; .. P = Ca. COR . 1. The same thing ...
... assumed equal to some number in the series 4 , 8 , 16 , & c . , which is greater than π 3 which is absurd . Therefore P is not greater than Ca , and in the same manner it may be shown not to be less ; .. P = Ca. COR . 1. The same thing ...
Strana 15
... assuming ( x ) of all positive values , we may find all the corresponding values of ( y ) , and measuring the positive values of ( y ) above the horizontal axis , and the negative below , the form of that part of the curve which lies to ...
... assuming ( x ) of all positive values , we may find all the corresponding values of ( y ) , and measuring the positive values of ( y ) above the horizontal axis , and the negative below , the form of that part of the curve which lies to ...
Strana 18
... assume , in conse- quence of the relation subsisting between it and ( x ) , then ( y ) and ( x ) are said to be functions of each other . If , in any proposition or problem , one quantity is considered as a function of another , the ...
... assume , in conse- quence of the relation subsisting between it and ( x ) , then ( y ) and ( x ) are said to be functions of each other . If , in any proposition or problem , one quantity is considered as a function of another , the ...
Strana 20
... assumes , when ( k ) is substituted for ( x ) , then K = A + Bk + Ck2 + Dk3 + & c . Now , since X = A + x ( B + Cx + Dx2 + & c . ) it is manifest , that if for all the intermediate values of a between ( k ) and ( o ) 20.
... assumes , when ( k ) is substituted for ( x ) , then K = A + Bk + Ck2 + Dk3 + & c . Now , since X = A + x ( B + Cx + Dx2 + & c . ) it is manifest , that if for all the intermediate values of a between ( k ) and ( o ) 20.
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.