( Hs ) 
GEN 
A 
A IR, a vehicle for found, but not the 
only one, 85. 
Difference of tone in founding bodies, 86. 
Echoes how produced, 90. 
Elaftic and non-elaftic bodies diftinguifh- 
ed, 88. 
Eolian lyre, its conftrudlion and adlion, 86. 
Organ and harpfichord, to make them play 
of themfelves, 91. 
A DDITION of algebraical quantities, 
283. 
Annuities, calculation of, 308 ; for lives, 
3 * 7 - 
Approxiinaiion, mode of, for difcovering 
roots of numeral equations, 302. 
Authors who have written on algebra, 
281, 282. 
Axioms, or felf-evident truths, 283. 
Binomial theorem, 293. 
Cardan’s rule for folving a cubic equa¬ 
tion, 299., 
Chances, dodlrineof, 3 15 ; throwing dice 
or balls, 315; chances of life, 3 1 6. 
Curve-lines, their general properties, 322. 
Definition and etymology of algebra, 281 ; 
definitions explanatory of the art, 282. 
Differential method, 313. 
Diophantus, the firft writer on algebra, 
281. 
Divifion of algebraical quantities, 284; of 
fractions, 286. 
Divifors, method of, 301. 
Equations limple, 288; quadratic, 289; 
their nature, 295; transformation of, 
A BORIGINAL America dcfcribed,42o. 
Algonquin woman, anecdoteof, 424. 
America, continent of, its boundaries and 
extent, 412 ; fuppofed to be imperfect¬ 
ly known to the ancients, ibid, pre¬ 
tentions of tile Welch to the firft difeo- 
very of it, ibid, of the Norwegians, 413; 
really difeovered by Columbus, ibid, ge¬ 
neral defcr'rption of, 416 ; divided into 
the North and South continent, ibid, 
climate, why fo different from the old 
continent, ibid, population uncertain, 
417 ; how firft peopled, 417, &c. cha¬ 
racter and manners of the inhabitants, 
as deferibed by variousauthors,4i8, &c. 
monuments of art in the interior parts, 
425. 
A.merica, North, when firft difeovered, 
428 ; progreflive fettlcment, 429-433 ; 
its boundaries, extent, &c. 433 ; divi- 
fions, 434; hiftory of the revolution, 
435-463; eftablifhment of the United 
States, 465. 
America, South, its divifions and pro¬ 
vinces, 434, 435. 
America, United States of, hiftory of the 
revolution which gave rife to the eftab- 
Vol. 1 , No. 53. 
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Reverberation of founds, 89. 
Sounds, how conveyed, 85 ; objections 
to Newton’s fyftem of fouVids, ibid, 
theory to which thefc objections give 
rile, 86; ftrength and foftnels of found, 
87 ; objections to the foregoing the¬ 
ory, 88. 
Speaking figures, how to make, 90. 
Speaking-trumpet, its aClion and ule, 89. 
ALGEBRA. 
296; limits of theirroots, 297 ; deprefi- 
fion and folution of, 298 ; iblution of 
recurring equations, 299 ; to folve a 
cubic equation by Cardan’s rule, ibid, 
to lolve a biquadratic by Des Cartes’s 
method, 300; by Dr. Waring’s, 301; 
conftruCtion of equations, by geome¬ 
try, 321. 
Evolurion, or extracting of roots, 286. 
Fractions, transformation of to others of 
equal value, 284; multiplication and 
divifion of, 285 ; continued fractions, 
306. 
Geometry, application of algebra to, 318. 
Increments, method of, 314. 
lntereftand annuities, 308. 
Involution, orraifing of powers, 286; Sir 
Ifaac Newton’s rule for raifing a bino¬ 
mial, 293. 
Italians, the firft cultivators of algebra in 
Europe, 281. 
Logarithms, 308. 
Multiplication of algebraical quantities, 
283 ; of fractions, 285. 
Permutations and combinations, 293.. 
AMERICA. 
lilhmcnt of them, 435-465 ; fketch of 
events which preceded the revolution, 
435 ; ftamp-adt, 437 ; duty on tea, &c. 
ibid, tea deftroyed at Bofton, 439; Bof- 
ton port-bill, ibid, meeting of congrefs, 
440; aCtions at Concord and Lexington, 
441 ; battle of Bunker’s hill, ibid, de¬ 
claration of congrefs, 442; Wafhington 
appointed commander in chief of the 
American army, 444 ; expedition into 
Canada, ibid, defeat of General Carle- 
ton, ibid. unfuccefsful attack on Que¬ 
bec, and death of General Montgomery, 
445; occurrences in Virginia, ibid. Bri- 
tilh governors expelled from fcveral pro¬ 
vinces, 446 ; Bolton evacuated by the 
Britilh, ibid. Americans declare them¬ 
felves independent, ibid, the Britilh 
foiled in their attempt on Charleftown, 
448; arrivalofcommiflionersfrom Eng¬ 
land,ibid. Americans defeated at Staten 
Ifland, 449 ; battle of the White Plains, 
450; Philadelphia taken by the Britifli, 
452; capture of Burgoyne and his army at 
Saratoga, 454; treaty of alliance be¬ 
tween France and America, 455 ; Phi¬ 
ladelphia evacuated by the Britilh, ibid. 
10 F 
D E X. 
s. 
Velocity of founds, 89. 
Vibration of mufical firings, 87 ; four 
founds produced from one firing, ibid. 
Whifpering gallery, conftruclion of, Sy- 
Pioblems which produce fimpleequations,, 
289 ; which produce quadratic equati— 
ons, 290; unlimited problems, 305. 
Progreffion, arithmetical, 292 ; geometri¬ 
cal, 293. 
Proportion, 291. 
Ratios, their nature and ufe, 290. 
Reverlion of feries, 302; recurring fcries,. 
3 l2> 
Roots of equations, their limits, 297 ; the’ 
impofliblc roots of an equation, 303. 
Signs tiled in algebra explained, 282. 
Solution of equations, 298 : of recurring 
equations, 209 ; of a cubic equation, 
ibid, of a biquadratic, by Des Cartes, 
300 ; by Dr. Waring, 301 .. 
Subtradlion of algebraical quantities, 283. 
Summation of feries, 309. 
Surds, or imperfedt roots,.294 ; binomial 
funis, 307. 
Transformation of fradfions, 294; of e- 
quations, 296. 
Variable quantities, 292. 
French fleet arrives on the coaft of Vir¬ 
ginia, 456 ; Charleftown taken by the 
Britilh, 459; Arnold deferts the Ame¬ 
ricans, 461 ; execution of Major Andre, 
ibid. Americans defeated at Guildford, 
463; adlion betweenthc Britilh andFrench 
fleets, 464; furrender of Lord Corn¬ 
wall is’s army at York-town, 465; treaty: 
of peace between England and the U- 
nited States, ibid, eftablifliment and 
boundaries of the United States, ibid, 
their conftitution and government, 466; 
manufadlories, &c. 467. 
Americus Vefpucius publifhes the lit ft 
written account of the new world, and 
thence gives nameto America,.416, 470. 
Boundaries and extent, 412. 
Cabot, John, fent on a voyage of difeo- 
very by Henry VII. 428. 
Cabot, Sebaftian, explores the ccafl of Bra- 
til, 428. 
Clavigcro, abbe, bis opinion relating to the 
firlt peopling of America, 418 ; bis re¬ 
marks on thecharadler and manners of 
the Americans, 421. 
Climate of America, 416. 
Columbus, Chriftopher, his birth and 
education, 
