The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves download book
The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves download book
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Author: James Hodgson
Number of Pages: 84 pages
Published Date: 01 Mar 2012
Publisher: Rarebooksclub.com
Publication Country: Miami Fl, United States
Language: English
ISBN: 9781130139877
File size: 45 Mb
Download Link: The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1758 Excerpt: ... AB=X then will BH = 1--x, and BC'= 1--x X x, = x--xx, by the Property of the Circle; whence-B C = x--xx. Again, because as A C: A B:: A H: A C; that is, as A C: x:: 1: A C; whence A C = xy and A C = #, it will be (by Proposition 1L of this x x X will be the Fluxion of the Portion A Nos the Cycloid, whose Fluent 2 x' = 2 A C, will be equal to the Arch A N; whence it follows, that the Length of the Semi.cycloid is equal to a A H, the Diameter of the generating Circle: For when B N, by flowing, arrives at H F, A C will become equal to A H. EXAMPLE X. Let it be required to find the Length of any Portion of the Ciflbid of Diodes. Let AD, the Diameter of the generating Circle See Figure following)xz put = dt AE = xy the Arch AC=2j, BC=j-, and A E=x j then will D E=B C = d--x; and because, from the I i Nature SECT. II. Containing the Use of Fluxions in the Quadrature of Curves or in finding the Areas of Curvilinear Spaces. PROPOSITION IV. Demonstration. Conceive the Line CBD to move with an uniform Motion along the Line ABi, constantly parallel to itself, 'till it comes'into the Place c b d, then will the Ordinates B C and B D describe the little Spaces B Cc b and B b d D, which ate the nascent Augments of the Spaces ABC and ABDG, generated in the fame very small Parcicle of Time; for while the Space ABC flowed into, or become A c b, the Space ABDG flowed into or became A b dG. From the Point C draw the Line C E parallel to the Base Line A B by then will the nascent Augment of the Curvilinear Area A B C be equal to the Rectangle C E b B-f the trilinear Space C c E j and inalmuch as Fluxions are in the last Ratio of their evanescent Decrements, if we imagine the right Line Line c b d, or, which is the fame thing, the Ordinates b c and b dt to return back towar
Read online The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves Buy and read online The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves Download and read The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent
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The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves by James Hodgson
Author: James Hodgson
Number of Pages: 84 pages
Published Date: 01 Mar 2012
Publisher: Rarebooksclub.com
Publication Country: Miami Fl, United States
Language: English
ISBN: 9781130139877
File size: 45 Mb
Download Link: The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves
---------------------------------------------------------------
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1758 Excerpt: ... AB=X then will BH = 1--x, and BC'= 1--x X x, = x--xx, by the Property of the Circle; whence-B C = x--xx. Again, because as A C: A B:: A H: A C; that is, as A C: x:: 1: A C; whence A C = xy and A C = #, it will be (by Proposition 1L of this x x X will be the Fluxion of the Portion A Nos the Cycloid, whose Fluent 2 x' = 2 A C, will be equal to the Arch A N; whence it follows, that the Length of the Semi.cycloid is equal to a A H, the Diameter of the generating Circle: For when B N, by flowing, arrives at H F, A C will become equal to A H. EXAMPLE X. Let it be required to find the Length of any Portion of the Ciflbid of Diodes. Let AD, the Diameter of the generating Circle See Figure following)xz put = dt AE = xy the Arch AC=2j, BC=j-, and A E=x j then will D E=B C = d--x; and because, from the I i Nature SECT. II. Containing the Use of Fluxions in the Quadrature of Curves or in finding the Areas of Curvilinear Spaces. PROPOSITION IV. Demonstration. Conceive the Line CBD to move with an uniform Motion along the Line ABi, constantly parallel to itself, 'till it comes'into the Place c b d, then will the Ordinates B C and B D describe the little Spaces B Cc b and B b d D, which ate the nascent Augments of the Spaces ABC and ABDG, generated in the fame very small Parcicle of Time; for while the Space ABC flowed into, or become A c b, the Space ABDG flowed into or became A b dG. From the Point C draw the Line C E parallel to the Base Line A B by then will the nascent Augment of the Curvilinear Area A B C be equal to the Rectangle C E b B-f the trilinear Space C c E j and inalmuch as Fluxions are in the last Ratio of their evanescent Decrements, if we imagine the right Line Line c b d, or, which is the fame thing, the Ordinates b c and b dt to return back towar
Read online The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves Buy and read online The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves Download and read The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook The Doctrine of Fluxions Founded on Sir Isaac Newton's Method Published by Himself in His Tract Upon the Quadrature of Curves ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent
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