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. 1902 Excerpt: ... the curves xl+y'= (f)' and pl + = (!)' 13. The area of p = a cos 3O, from o to Jjr, is Viffi'. 14. Show that the area of p--a (sin 28-f-cos 26), from o to zn, is ita1. 15. The area of p cos 0--a cos 26, from o to it, is i(2--Jff)aJ. 163. We come now to consider the area generated by a straightline segment which moves ...
Read More
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. 1902 Excerpt: ... the curves xl+y'= (f)' and pl + = (!)' 13. The area of p = a cos 3O, from o to Jjr, is Viffi'. 14. Show that the area of p--a (sin 28-f-cos 26), from o to zn, is ita1. 15. The area of p cos 0--a cos 26, from o to it, is i(2--Jff)aJ. 163. We come now to consider the area generated by a straightline segment which moves in a plane, under certain general conditions. In rectangular coordinates we. have considered the area generated by the moving ordinate to a curve. In polar coordinates the area considered was generated by a moving radius vector. In the former case the generating line moves parallel to a fixed direction, in the latter it passes through a fixed point. A point Q is taken on the tangent at P to a given curve PP', such that PQ--t. To find the area bounded by the given curve, the curve QQ' described by Q, and two positions PQ, P'Q' of the generating line. the angle AO. Draw the chord PP' and the circular arcs QM, Q'M' with / as a center. Then A A is equal to the area of the circular sector QIM, plus a fraction of the area of the triangle PIP', plus a fraction of the area QM Q'M'. Or, in symbols, AA = $(/-St?AO _f_ Agt. gt sin 40 + /, ry+ o-vy! _ (/_ 6tyA6, 2 2 where _/J, are proper fractions. Observing that At, St, and S't converge to o when A0(=)o, divide by AO and let A0(=)o. Then dOV' or = /V0. Hence between the limits 0 = a, 0 = ft the area swept over by / is A = '2dO. When the law of change of /, the length of the tangent, is given as a function of 0, the area can be evaluated. If / = /(O) be this relation, the curve / = f0), considering / as a radius vector and 0 the vectorial angle, is called the directing or director curve of the generating line. EXAMPLES. 1. Show that the area swept over by a line of constant length a laid off on...
Read Less
Add this copy of An Elementary Text-book on the Differential and to cart. $28.53, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
Add this copy of An Elementary Text-Book on the Differential and to cart. $31.78, new condition, Sold by Books2anywhere rated 5.0 out of 5 stars, ships from Fairford, GLOUCESTERSHIRE, UNITED KINGDOM, published 2022 by LEGARE STREET PR.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of An Elementary Text-book on the Differential and to cart. $33.01, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of An Elementary Text-Book on the Differential and to cart. $37.10, new condition, Sold by Just one more Chapter rated 3.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 2022 by Legare Street Press.
Add this copy of An Elementary Text-book on the Differential and to cart. $38.05, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
Add this copy of An Elementary Text-Book on the Differential and to cart. $42.78, new condition, Sold by Books2anywhere rated 5.0 out of 5 stars, ships from Fairford, GLOUCESTERSHIRE, UNITED KINGDOM, published 2022 by LEGARE STREET PR.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of An Elementary Text-book on the Differential and to cart. $43.31, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of An Elementary Text-Book on the Differential and to cart. $43.85, new condition, Sold by Paperbackshop International rated 1.0 out of 5 stars, ships from Fairford, GLOS, UNITED KINGDOM, published 2022 by LEGARE STREET PR.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of An Elementary Text-Book on the Differential and to cart. $49.61, new condition, Sold by Just one more Chapter rated 3.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 2022 by Legare Street Press.
