Items related to New series of The mathematical repository Volume 6
Synopsis
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. 1835 Excerpt: ...equation of the surface. " duy being always the horizontal plane, if through the axe iter prolonged and Gq a plane be made to pan it will cut (lie surfaces along an edge va'ic', perpendicular to the axe and parallel to Gq. Through this edge draw a horizontal plane, which meets in the points //, M &c. the ordinatej B6, Km, &c. and through these points!/, M', &c. draw the straight lines b'a', M'w', &c. parallel to Mar; denote the ordinates F', W'm', M'n by, y, z respectively. Let the edge Ab meet m' in a', and put Yaf ca--e a being the point where Ab meets rn'. Then we shall have y--This equation of the surface e tan p is, except that of the plane, the most simple po&sible. " We may easily find the distance Fg = f)of this new horizontal plane. For, let x--ra' = ca--e, y--a'A'--ja s g cos m, and z will be = /. Then. ef, a cos m tan p tan a a co» m---; or /--s cos m tan p--1, e tan p J 6 r tan p--tan q by giving g its value found in above.. " We can readily discover the value of the angle Bac, and hence that which the plane Bac makes with the horizontal Ca6: and thus we may find the equation of the quadriiatere gauche referred to the plane drawn by two of its contiguous sides. But it is easy to find it directly: though on account of its greater complexity compared with that already given we shall omit k here, and more especially as it does not in any degree furnish us with new views or properties of the surface. " We may desire to know the minimum of all the elements Ab, NP, CD, &c. of the twisted quadrilateral. In the triangle j'Mp the angle NMP is constant; let it be called M. Let also Nm--Ar--1),. bx sin K Mi' or y--which must be a minimum. Hence axdx tin K--aa tin ft J i i c a sin L cos M D,. _ cos Mar--o, au...
"synopsis" may belong to another edition of this title.