The place of the elementary calculus in the senior high-school mathematics : and suggestions for a modern presentation of the subject . the Curve to beindefinitely small, and draw theright Lines NQ, NR parallel toMP, AP; I call MP, m; PT, t;MR, a; NR, e; and grve Names toother Lines useful to our purpose,determined from the particularNature of the Curve; and thencompare MR, NR expressed by Calculation in an Equation, and by their means MP, PT them-selves; observing the following Rules at the same time. 1. I reject all the Terms in the Calculation, affected with anyPower of a or e, or with the
The place of the elementary calculus in the senior high-school mathematics : and suggestions for a modern presentation of the subject . the Curve to beindefinitely small, and draw theright Lines NQ, NR parallel toMP, AP; I call MP, m; PT, t;MR, a; NR, e; and grve Names toother Lines useful to our purpose,determined from the particularNature of the Curve; and thencompare MR, NR expressed by Calculation in an Equation, and by their means MP, PT them-selves; observing the following Rules at the same time. 1. I reject all the Terms in the Calculation, affected with anyPower of a or e, or with the product of them; for these Terms willbe equal to nothing. 2. After the Equation is formed, I reject all the Terms whereinare Letters expressing constant or known Quantities; or which arenot affected with a, or e; for these Terms brought over to one sideof the Equation will be always equivalent to nothing. 3. I substitute a for m {MP), and t (PT) for e; by which meansthe Quantity of PT will be found. When any indefinitely small Particle of the Curve enters theCalculation, I substitute in its stead a Particle of the Curve properly. 24 Elementary Calculus in Senior High-School Mathematics taken; or any right Line equal to it, because of the indefinite Small-ness of the Part of the Curve. 4 By means of his differential triangle method, Barrow could findthe tangent to a curve at any point. He lacked a classified set offormulas which would have facilitated this work. Also, there wasat this time no rigorous treatment of the theory of limits. Thismethod of Barrows justifies the presentation of the derivative asthe limit of a geometric ratio to pupils who possess only an intuitiveand elementary knowledge of limits. Isaac Newton. The third general step in the development of thecalculus was the invention of fluxions by Newton (c. 1665).5 The method of fluxions played a very important part in the de-velopment of the calculus. A little insight into the nature of thesubject will now be given
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