ISBN: 1236203917

[EAN: 9781236203915], Neubuch, [PU: RareBooksClub], BENJAMIN WILLIAMSON,WORLD, This item is printed on demand. Paperback. 74 pages. Dimensions: 9.7in. x 7.4in. x 0.1in.This historic book … More...

[EAN: 9781236203915], Neubuch, [PU: RareBooksClub], BENJAMIN WILLIAMSON,WORLD, This item is printed on demand. Paperback. 74 pages. Dimensions: 9.7in. x 7.4in. x 0.1in.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. 1891 Excerpt: . . . section is a similar and similarly situated 183. Elliptic Paraboloid. --The corresponding results for the elliptic paraboloid can bo deduced from the preceding by adopting the usual method of such derivation: viz. , by taking ai pc, b2 qc, and afterwards making c infinite; observing that in this case the ratio--. becomes unity. c J Making these substitutions in (4), it becomes V ir pqh f 1---A or irh2 pq, since d 00. Hence, if a constant length be measured on any diameter of an elliptic paraboloid and a conjugate plane drawn, then the volume of the segment cut from the paraboloid by the plane is constant. Again, the area of an elliptic section by (3) is, T, 2A h2 ndbc (zh h irabl-r-- I or For a more direct investigation the student is referred to a memoir On some Properties of the Paraboloid, Quarterly Journal of Mathematics, June, 1874, by Professor AJlman. On making the same substitutions, this becomes for the paraboloid 27r Spq sino) Now, if we suppose a cylinder to stand on this section, the volume of the portion cut off by the parallel tangent plane to the paraboloid is obtained by multiplying the area of the seotion by h sin u; and, consequently, is 2jt pqh1, i. e. is double the corresponding volume of the paraboloid. This is an extension of the theorem of Art. 180. Examples. 1. Prove that the volume of the segment out from a paraholoid hy any plane is fths of that of the circumscribing cone standing on the section made by the plane as base. 2. A cylinder intersects the plane of xy in an ellipse of semiaxes OA a, OB , and the plane of xz in an ellipse of semiaxes OA--a, 00 c; the edges of the cylinder being parallel to BG; find the volume of the portion of the cylinder bounded by the three co-ordinate planes. Ana. dbc. . . . This item ships from La Vergne,TN.<

2012, ISBN: 1236203917

[EAN: 9781236203915], Neubuch, [PU: Rarebooksclub.com, United States], Language: English Brand New Book ***** Print on Demand *****. This historic book may have numerous typos and missing… More...

[EAN: 9781236203915], Neubuch, [PU: Rarebooksclub.com, United States], Language: English Brand New Book ***** Print on Demand *****. 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. 1891 Excerpt: .section is a similar and similarly situated 183. Elliptic Paraboloid.--The corresponding results for the elliptic paraboloid can bo deduced from the preceding by adopting the usual method of such derivation: viz., by taking ai =pc, b2 = qc, and afterwards making c infinite; observing that in this case the ratio--. becomes unity. c J Making these substitutions in (4), it becomes V = ir /pqh f 1---A or irh2 /pq, since d = 00. Hence, if a constant length be measured on any diameter of an elliptic paraboloid and a conjugate plane drawn, then the volume of the segment cut from the paraboloid by the plane is constant. Again, the area of an elliptic section by (3) is, T, /2A h2 ndbc (zh h? irabl-r--- I or For a more direct investigation the student is referred to a memoir On some Properties of the Paraboloid, Quarterly Journal of Mathematics, June, 1874, by Professor AJlman. On making the same substitutions, this becomes for the paraboloid 27r Spq sino) Now, if we suppose a cylinder to stand on this section, the volume of the portion cut off by the parallel tangent plane to the paraboloid is obtained by multiplying the area of the seotion by h sin u; and, consequently, is 2jt /pqh1, i. e. is double the corresponding volume of the paraboloid. This is an extension of the theorem of Art. 180. Examples. 1. Prove that the volume of the segment out from a paraholoid hy any plane is fths of that of the circumscribing cone standing on the section made by the plane as base. 2. A cylinder intersects the plane of xy in an ellipse of semiaxes OA = a, OB =, and the plane of xz in an ellipse of semiaxes OA--a, 00 = c; the edges of the cylinder being parallel to BG; find the volume of the portion of the cylinder bounded by the three co-ordinate planes. Ana. dbc.<

2012, ISBN: 1236203917

[EAN: 9781236203915], Neubuch, [PU: Rarebooksclub.com, United States], Language: English Brand New Book ***** Print on Demand *****.This historic book may have numerous typos and missing … More...

[EAN: 9781236203915], Neubuch, [PU: Rarebooksclub.com, United States], Language: English Brand New Book ***** Print on Demand *****.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. 1891 Excerpt: .section is a similar and similarly situated 183. Elliptic Paraboloid.--The corresponding results for the elliptic paraboloid can bo deduced from the preceding by adopting the usual method of such derivation: viz., by taking ai =pc, b2 = qc, and afterwards making c infinite; observing that in this case the ratio--. becomes unity. c J Making these substitutions in (4), it becomes V = ir /pqh f 1---A or irh2 /pq, since d = 00. Hence, if a constant length be measured on any diameter of an elliptic paraboloid and a conjugate plane drawn, then the volume of the segment cut from the paraboloid by the plane is constant. Again, the area of an elliptic section by (3) is, T, /2A h2 ndbc (zh h? irabl-r--- I or For a more direct investigation the student is referred to a memoir On some Properties of the Paraboloid, Quarterly Journal of Mathematics, June, 1874, by Professor AJlman. On making the same substitutions, this becomes for the paraboloid 27r Spq sino) Now, if we suppose a cylinder to stand on this section, the volume of the portion cut off by the parallel tangent plane to the paraboloid is obtained by multiplying the area of the seotion by h sin u; and, consequently, is 2jt /pqh1, i. e. is double the corresponding volume of the paraboloid. This is an extension of the theorem of Art. 180. Examples. 1. Prove that the volume of the segment out from a paraholoid hy any plane is fths of that of the circumscribing cone standing on the section made by the plane as base. 2. A cylinder intersects the plane of xy in an ellipse of semiaxes OA = a, OB =, and the plane of xz in an ellipse of semiaxes OA--a, 00 = c; the edges of the cylinder being parallel to BG; find the volume of the portion of the cylinder bounded by the three co-ordinate planes. Ana. dbc.<

ISBN: 9781236203915

Paperback, [PU: Rarebooksclub.com]