GENERAL INDEX. 
975 
GEOMETRY, 417-446. 
LGEBRA, Its application to geome¬ 
try, 439. 
Angles and triangles, 424. 
Apollonius and Archimedes, 417, 19, 21. 
Arabian geometricians, 417. 
Axioms, or felf-evident truths, 425. 
Cavalerius, the inventor of the geometry 
of indivifibles, 420, 421. 
Compafs, geometry of, 443. 
Cycloidal curves, 440. 
Definitions and Principles, 429; of the 
cycloidal curve, 440. 
Egyptians, fuppofed to be the inventors of 
geometry, 417. 
Euclid’s Elements of Geometry, 417. 
Figures of various kinds, 424. 
Fluxions, their invention and ufe, 422. 
Geometry, definition, origin, and ancient 
ftate, 417 i divifions and ufes, 418 ; geo¬ 
metry of infinites, 418 ; examination the 
method of the ancients, 418, 19, 20 ; 
geometry of indivifibles, 420; definitions 
and principles of geometry, 424 ; of geo¬ 
metrical proportion, 432 j application of 
algebra to, 439 , of cycloidal curves, 440; 
of the compafs, 443. 
Creeks received geometry from the Egyp¬ 
tians, 417. 
Infinites and infinitefimals, 420 & feq. 
Leibnitz, Mr. 420; his opinion on the doc¬ 
trine of infinites, 423. 
Line, ftraight and curved, 424, 429. 
Locke’s remarks on ihe doflrlne of Infinite¬ 
fimals, 420. 
Newton, Sirlfaac, 41S; inventor of fluxions, 
422- 
Planes and folids, 437. 
Plato highly honoured geometry, 417. 
Point, how to define, 424. 
Poftulates, 425. 
Problems, 426. 
Proportion, geometrical, 432. 
Romans paid little attention to geometry, 
417- 
Theorems, 429; on the cycloidal curve, 
440. 
Wallis’s Arithmetica InfinitoRim, 421. 
Adolphus of Naflau, 483. 
Albert duke of Aullria, 482 ; em¬ 
peror, 483. 
Albert II. 486. 
Alemanni, formidable to the Romans, 470; 
fubdutd by Charlemagne, 471. 
Alexander I. emperor of Ruflia, 519. 
Alphonfo ol Caftile, 482. 
Anne queen of England, 500 ; fupports the 
emperor [ofeph, j inclines to make 
peace, 503 j which is figned at Utrecht, 
504. 
Arminius, a noble German, his unfuccefs- 
ful revolt, 470. 
Aufterlitz, battle of, 519. 
Bannat, war in that province, 507. 
Bannier, a Swedifh general, 494 j his death, 
495. _ 
Bavaria in arms againft the emperor, 5COJ 
fort.tude of the eleftor, 501; the cala¬ 
mities of the country, 502 ; deprived of 
territory by the treaty of Luncville, but 
joins the French in the war that fol¬ 
lowed, 518 ; made a king, 520. 
Bavarian and Salzburgh mountains, 464. 
Bergftrafs mountains, 463. 
Bernadette, French general, 5115 ambaf- 
fador at Vienna, 512. 
Bernard duke of Weimar, 494* 
Black Foreft, 463. 
Black Mountains, or Swabian Alps, 463. 
Blocklberg mountains, 463. 
Boden See and Chiem See, 463. 
Boleflaus firft king of Poland, 474. 
Bonapartej his rapid fuccefles in Italy, 509 ; 
defeats the archduke Charles, and forces 
the emperor to an accommodation, 510 ; 
gains the battle of Marengo, 515 ; (em- 
petor,) feizes Hanover, 518 ; enters Vi. 
tnna, and gains the battle of Aufterlitz, 
519 ; which occafions the peace of Pref- 
burgh, 520. 
Caefar attacks the Germans, 469. 
Campo Formio, treaty of, 511. 
Carpathian mountains, 464. 
CafTano, battle of, 501. 
Catinat, French general, 499. 
Charlemagne, emperor of the weft, 471, 
Charles of Luxemburg, 485. 
Charles duke of Burgundy, 486. 
Charles V. 487 j oppofes the reformation ; 
a league againft him, diflblved by the 
death of the pope, 488 3 fixes the knights 
of St. John at Malta, his diftimulation, 
makes peace with France, and prepares 
10 defend himfelf againft the Turks, 
,^89; rcftoics the king of Tunis, invades 
GERM ANY, 462-528. 
France, and again makes peace; chaftifes 
the inhabitants of Ghent, 490 ; forced 
to make peace with the proteftants, re¬ 
tires from all public bufinefs, and dies, 
491 ; farther account of his proceedings 
againft the proteftants, 524. 
Charles Guftavus, king of Sweden, 496. 
Charles archduke of Auftria, his ineft'eflual 
endeavours to obtain the crown of Spain, 
500 ; duke of Milan, 502 ; emperor of 
Germany as Charles VI. 503 ; purfues 
the war for fonie time without the aflift- 
ance of England, but at length figns the 
treaty of Raftadt ; his wars with the 
Turks, dies, 504. 
Charles VII. 504; his death, 505. 
Charles archduke of Auftria, takes fort 
Kelli, but is thrice defeated, 510; his 
difpofitions in the enfuing campaign, 511; 
viftorious, 512 ; driven out of Swilfer- 
land, 513; again defeated, and figns an 
armiftice in order to fave Vienna, 516 j 
commands with little fuccefs initaly, 518. 
Conrad emperor of Germany, 471 ; Conrad 
II. 475; Conrad III. 478; Conrad IV, 
481. 
Conradin and Conrad, the laft of the Swa¬ 
bian dynafty, 482. 
Conftance, Plau, and Schwerin, lakes, 
463- 
Cuftine, French general, 509. 
Danube river, 462. 
Drufus, his exploits againft the Germans, 
469. 
Dumouriez, gains the battle of Jemappe, 
takes Bruffels, &c. 509. 
Elbe and Ems rivers, 462. 
Eugene, prince, defeats the Turks at Zenta, 
takes Villeroi prifoner, 500; defeated, 
501 ; again vidtorious, 503. 
Europe in general, fuppofed to have been 
fotmerly colder-than at prefent, 464; 
accounted for, 465. 
Erzgeburg, or Metallic Mountains, 463. 
Ferdinand I. fucceeds upon the abdication 
of Charles V. 491; his reign and death, 
492. 
Ferdinand II. 493 ; dies, after gaining the 
name of Apoftolic Emperor for perfecut- 
ing the proteftants, 494. 
Ferdinand III. 494; figns the peace of 
Weftphalia, 495 y his death, 496. 
Ferdinand duke of Brunfwick, his ill- 
judged manifefto, 508 ; unfuccefsful in 
the war of 1805, 518. 
Ferdinand V. eledtor palatine, J25. 
Fotefts, 462, 464. 
Francis I. of France, the rival of Charles 
V. emperor of Germany, 488; taken 
prifoner, but being releafed renew-s thO. 
war in Italy, and at length makes peace, 
489 j difpofleftes the duke of Savoy, 490 ; 
another war with the emperor begun and 
ended, 491. 
Francis I. of Germany, 503. 
Francis II. at war with France, 508; his 
Italian rfates attacked, 509; after tlie 
lofs of five armies, liftens to terms of 
peace, 510; figns the treaty of Campio 
Formio, but the war is foon renewed, 
511; caufes thereof, 512; rejedls the 
propofals of Bonaparte, 513; refufes to 
ratify a treaty made by count St. Julian, 
515; the imperial family quit Vienna, 
which is faved for that time by an ar¬ 
miftice, 516 ; figns the treaty of Lune- 
ville, 517; but foon renews the war, 
518 j lofes his capital, and the battle of 
Aufterlitz, 519 ; follow-ed by the peace 
of Prelburgh, 520 j refigns the title of 
Emperor of Germany, 524. 
Frederic Barbarolfa, 478 j his crufade, and 
death, 479. 
Frederic II. 481. 
Frederic of Auftria, 484. 
Frederic of Brunfwick, 485. 
Frederic HI. 486. 
Frederic the Wife, duke of Saxony, 488. 
Frederic king of Pruffia, 505, 519. 
French revolution, ineft'edtually oppofed by 
Jofeph II. and Francis II. 508. 
George II. gains the battle of Dtttingsn,305. 
Germanicus, his exploits in Germany, 470. 
Germany, its limits, ancient ftate, and pre'- 
fent appearance, 462 j rivers and moun¬ 
tains, 463; forefts, 464; primitive hif- 
tory, 464; had no letters, no arts, no 
cities, in the time of Tacitus, 465 j re¬ 
markable powers of the early magiftrates, 
467; women and religion, 468; arms, 
469 ; wars with the' Romans, 469 ; 
partly fubdued by them, 470 j but to¬ 
tally by Charlemagne, 470; throne be¬ 
comes imperial, 471 ; interregnum and 
anarchy previous to the acceflion of the 
Auftrian dynafty, 482; the empire de¬ 
clared independent of the pope, 484; 
ceremony at elediions as fettled by the 
golden bull, 485 ; divided into ten circles, 
487; the thirty-years war, 493; peace 
of Weftphalia, 495 ; famine, 505 ; treaty 
of Prelburgh, 520 ; conftitution and go¬ 
vernment, 520 ; power of the emperor,, 
523 5 no emperor of Germany at prefent, 
524 5 - 
