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' = ...
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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
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Add this copy of The Doctrine of Fluxions Founded on Sir Isaac Newton's to cart. $61.61, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2011 by Nabu Press.
