Press: RareBooksClub.com (March 6, 2012)
Author Name:Group, Books
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.
1757 Excerpt: ...
Qy Estion 414 answered by the Proposer, Mr.
glNCE the Stress or Pressure upon the Prop ED is (by Mechanics) as 5--(supposing B F perpendicular to E D), the Force in the perpendicular Direction, whereby the Beam tends to break at E, will be as = (it being to the absolute Force, in the Direction DE, as B E to B F).
But the Strength of (or the whole Force ne» cessary to break) the Beam at E, is known to be as '---: which 1 At X BE' j is to g-g the Force above-mentioned, In the Proportion of A£ Al ".s" to A E X B E' or 1 t0 A wnence 07 tne Question) A E is to be a Mtmmua, and consequently BE a Maximum t But B E is to the Sine of the Angle D in the given Ratio of E D to the Sine of B; whence it is evident that B E will be a Maximum when the Sine of D is so, or when D itself is a Right-Angle.--Therefore, having made B K perpendicular to BC and =fc the given Length of DE, draw KE parallel to BC, meeting A B in E, io Jhall E be the Place where the End of the Prop must stand.
Much after the fame Manner the Problem was solved by Mess.
Botbavt, Cbarlton, Holltday, Trott, and JVatson j all of whom determined the Angle BDE to be a right one, X.
Question 41 5 answered by Mr.
LET S = 1000 = the Sum proposed; r (1,05)) r= the Amount of T7.
in one Quarter, and n = the Number of Quarters required; then the Amount of the Sum S will be S r ", and the AmStint of all the quarterly Payments (exclusive of that due at the End Of » Quarters) =S: r " 1 + ' "r1 3 r " 3 + 4 r" f.
continued to i»--1 Terms; the Sum Of all whish will be' f C 3 this, by the Nature of Question, must be equal to r n (the Sum n paid at the End of n Quarters, and its Interest for the fame Quarter) s Hence Log.
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