B R I 



;-. = -i- - 2i+ * -i + fcc. 



as as T a-* a 5 n 



__ _ ,__ __ 



' 2 a* 4- ;r* r a a* 4a" ~*~ 8 3 



In expanding a trinomial, quadrinonrial, mutiuomial, collider every 

 term, except the 1st., as the 2d term of a binomial, and then proceed ac- 

 cording to the rule. 



E.x. 1. (a 4- b 4- c) (a 4. 6 -j- c) = az 4. 2 a. 5 4. e 4. (b 4. c)t 

 a -{- 6 4. -f 2 a b + 2 a c -j- 2 & c. 



2. (a 4- i -f c)s .(a 4. b 4- c}3 a -f 3 . & 4- c -f 3 . (6 -}- c)s 

 4- (6 4- c)3. 



3. ( a 4. i 4. c 4- d 4. &c.' w = a w 4- a . (6 -J- c 4. d 4. &c.) 



4. n. - a (6 + c 



(6 4. c 4. <? 4- &c.) 3 4- &c. but see Demoivrc's Analyt. p. 87. 



BISSEXTILE. See Calendar. 



BOILING point of various liquids. See Heat. 



BRIDGE. See ArcJies equilibrium of. 



BRIDQES. 



List of a few of the mast remarkable modern Bridges, with the date of 

 tlieir erection, the lengths of the chord and verged s\ne of the centre arch 

 in feet, fyc. $c. 



STONE BRIDGES. 



No. 



Place. Date. Arches. Chord. Ver. sin. Curve. 



Avignon, Rhone ............ 1188 ... 18 ...... 110% ...... 45% circular. 



Brioude, Allier ............... 1451 ... ...... 183 ...... 70^ circular. 



This is the largest stone arch in existence. 

 Florence, Arno ............... 1569 ... 1 ...... 95^ ...... 14% elliptical. 



The Rialto, Venice ....... .. 1591 ... 1 ...... 96% ...... 20^ 



Grenoble, Drac ............... 1611 ... ...... 150 ...... 62% circular. 



Orleans, Loire ............... - ... 9 ...... 106^ ...... 29% false ellipse. 



Pont Royal, Seine ............ 1685 ... 5 ...... 82 ...... - 



Neuilly ........................... 1774 ... 5 ...... 128 ...... 32 false ellipse. 



Nantes, Seine .................. 1765 , 3 ...... 128 ...... 33^ elliptical. 



43 



