Overview

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. 1770 Excerpt: ...P and, and the product will be the content of the spindle FDGN. 4 E That of the spindle, e being the height FI of the segment. Corollary I. If d be supposed = c, the ellipse will become a circle, and accordingly the theorems above given will become the fame with those before found for the circular spindle. Co Example. The axes of an ellipse being 50 and 30, required the solidity of a spindle generated from an arc Corollary II. Is H coincide-with C, b will vanish, a will be s= r, and the theorems will become the fame with those before found for the spheroid. Corollary III. Putting D = DN the greatest, and d = KO the least diameter of the frustum, h = HI its height, CsCH the central distance, / 5= the elliptic semi-segment KDM, and =-78539 &c. Then, in the soregoing theorems, h=x, baC, d=C+iD, area HIKD = s + db, cXViDD+DC-idd-dc'anda=is/iDD+DC-idd-d which values being substituted in the theorems above, give j-nh X zDD + dd--8Cx--D+d+j- or the value of the frustum, or Kalf a cask in the form os the middle zone of an elliptic spindle; and nl X 2DD--8CX--D+-for half the spindle when S s the area DFH, and lz=.HF. Corollary IV. But in real practice, such as cask gauging, none of these rules can be used, because that we have not given either the axes of the ellipse or the central distance; and to accommodate rules to that purpose we must introduce another dimension of a frustum besides its length and greatest and least diameters Thus, putting m z= P Q, the diameter through R the middle of the length HI, and the other letters before. Then, by the property of the ellipse, C+i Dx--C+jd 1:: TiDx-t+T!1 . twice 4 X C+iM1--3 X 6+il1 =e arc of it about its chord parallel to, and at the distance of, 9 from the transverse axe. Here 15-9-6 = DH= the...

Full Product Details

9781232364351

Table of Contents

Reviews

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available