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BRAZIL.

dwt. grs. 8 cts. m. $ cts. m. Johannes, half in proportion,

16.00,0 17.06,4 Dobraon, • • - • • | 34 12 30.66,6 32.70,6 Dobra,

18 6

| 16.22,2 17.30,1 Moidore, half in proportion, • •| 6 22 6.14,9 6.55,7 Crusade,

1 .59,8 .63,5 BRUNSWICK. Pistole, double in proportion,

4 211

4.27,1 4.54,8 Ducat, . .

2 54

2.09,2 2.23,0 COLOGNE. Ducat, • .

2.12,5 | 2.26,7 COLOMBIA. Doubloons, .

17 9 14.56,0 15.53,5 DENMARK. Ducat, current,

1.70,5 1.81,2 Ducat, specie,

2.12,5

2.26,7 Christian d'Or, -

3.77,0 4.02,1 East INDIES. Rupee, Bombay, 1818,

7 11 6.65,4 7.09,6 Rupee, Madras, 1818, •

6.66,7 7.11,0 Pagoda, Star, · · ·

2 43
1.68,9

1.79,8
ENGLAND.
Guinea, half in proportion, -

5 84 4.79,9 5.07,5 Sovereign, ..

..
.
. ..

5 25

4.57,0 4.84,6 Seven Shilling Piece, • • • 1 19 1.60,0

1.69,8
FRANCE.
Double Louis, coined before 1786, 10 11 9.08,7 9.69,7
Louis, coined before 1786, -

5 55 4.54,1 4.84,6
Double Louis, coined since 1786, 9 20 8.59,0 9.15,3
Louis, coined since 1786, ... 4 22 4.29,5 4.57,6
Double Napoleon, or 40 francs, -

8 7

7.23,2 7.70,2 Napoleon, or 20 francs,

3.61,6 3.85,1 FRANKFORT ON THE MAINE. Ducat, - - - -

2 54 2.13,7 2.27,9 GENEVA. Pistole, old, • • • •

4 74 3.73,7 3.98,5 Pistole, new, - - - - 3 15$ 3.23,2

3.44,4
HAMBURG.
Ducat, double in proportion,

2 54
2.13,7

2.27,9
GENOA.
Sequin, - - - - - 2 54 2.15,8 2.30,2

HANOVER. Double Geo. d'Or, single in proportion, 8 13 | 7.48,2 | 7.87,9 |

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101

grs. $ cts, m. $ cts. m. Ducat, -

532 .15,4 2.29,6 Gold Florin, double in proportion,

2 1.57,6 1.67,0 HOLLAND. Double Ryder, - - - - | 12 21 | 11.44,2 | 12.20,5 Ryder, - - - -

6 9 5.66,5 6.04,3 Ducat, -

2 58 2.13,3

2.27,5 Ten Guilder Piece, Five do. in pro.,

3.78,0

4.03,4 MALTA. Double Louis, • •

10 16 8.69,9 9.27,8 Louis, • • • • •

5 8 4.36,4 4.85,2 Demi Louis, - - - -

2 16

2.20,2 2.33,6 MEXICO. Doubloon, shares in proportion, 17 9 14.56,0 15.53,5

MILAN. Sequin, .

2 58 2.15,6

2.29,0 Doppia or Pistole, . ,

4 11 3.57,2 3.80,7 Forty Livre Piece, 1808,

8 8 7.26,1 7.74,2 NAPLES. Six Ducat Piece, 1783,

5 16 4.92,5 5.24,9 Two Ducat Piece or Sequin, 1762, 1 204 1.51,1

1.59,1 Three Ducat Piece or Oncetta, 1818,

2.34,7

2.49,0 NETHERLANDS. Gold Lion or 14 Florin Piece, - 5 74 4.73,1 5.04,6 Ten Florin Piece, 1820,

4 78

3.76,6 4.01,9 PARMA. Quadruple Pistole, double in proportion, 18 9 15.59,6 | 16.62,8 Pistole or Doppia, 1787, .

4 14

3.93,5 4.19,4 Pistole or Doppia, 1796,

4 14 3.87,5 4.13,5 Maria Theresa, 1818, -

3.62,4 3.86,1 PIEDMONT. Pistole, coined since 1785, half in pro., 5 20 5.07,5

5.41,1 Sequin, half in proportion,

2 5

2.13.7 2.28,0 Carlino, coined since 1785, half in pro., 296 25.63,2 27.34,0 Piece of 20 francs, called Marengo, 4 34 3.34,1 3.56,4

POLAND.
Ducat, - -

2 52
2.13,7

2.27,5 PORTUGAL. Dobraon, . .

34 12 30.66,6 32.70,6 Dobra, - - - - - 18 6 16.22,2 | 17.30,1 Johannes, . .

18 0 16.00,0 17.06,4 Moidore, half in proportion,

6.14,9 6.55,7 Piece of 16 Testoons or 1600 R

1.99,2 2.12,1 Old Crusado of 400 Rees,

.84,9 .58,5 New Crusado of 480 Rees, .

164 .59,8 .63,5 Milree, coined in 1775,

1991 .73,2 78,0

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Prussia.

dwt. grs. 1 $ cts. m. $ cts. m. Ducat, 1748, - - - - 2 59 2.13,7

2.27,9 Ducat, 1787, - - - - 2 58 2.12,5 2.26,7 Frederick, double, 1769,

- 1 8 14 7.47,5 7.95,5 « 1800, - - 8 14 7.45,4 7.95,1 single, 1778,

3.74,9 3.99,7 6 1800, - - 4 7 3.72,5

3.97,5 Rome. Sequin, coined since 1760,

2.10,9 2.25,1 Scudo of Republic, . . .

14.82,8 15.81,1 Russia. Ducat, 1796,

2.15,0

2.29,7 Ducat, 1763, - - -

2.12,5

2.26,7 Gold Ruble, 1756, - -

.90,9 .96,7 Gold Ruble, 1799, • •

.69,1 .73,7 Gold Poltin, 1777, - -

.33,1 .35,5 Imperial, 1801, - - -

7.34,9 7.82,9 Half Imperial, 1801, - -

3.68,9 3.93,3 SARDINIA. Carlino, half in proportion, .

8.88,1 9.47,2 Saxony. Ducat, 1784, -

2.12,5 2.26,7 Ducat, 1797,

2.13,7 2.27,9 Augustus, 1754, - .

3.68,5

3.92,5 Augustus, 1784, - -

3.72,5

3.97,4 Sicily. Ounce, 1751, - - . | 2 204 2.35,1

2.50,4 Double Ounce, 1758, • . - I 5 17 4.72,7

5.04,4 SPAIN. Doubloon, 1772, parts in proportion, | 17 84 15.03,0

16.02,8 Doubloon,

14.56,0

15.53,5 Pistole,

3.64,0 3.88,4 Coronilla, Gold Dol. or Vintern, 1801, i 3* .92,1

SWEDEN.
Ducat, - - - - - - 2 5 2.09,7

SWITZERLAND.
Pistole of the Helvetic Republic, 1800,

4.56,0 Treves. Ducat, • - - - - - 2 58 2.02,5 2.26,7

Turkey. Sequin Fonducli of Constan’ple, 1773, 2 58 1.74,9 1.86,8 Sequin Fonducli of Constan'ple, 1789, 2 5$ | 1.73,3

1.84,8 Half Misseir, 1818, - -

18+ .49,1 Sequin Fonducli, - - - 2 5 1.71,7 1.83,0 Yeermeeblekblek, - - - - 3 19 1 2.84,0 3.02,8 l

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TUSCANY.

dwt. grs. Zechino or Sequin,

| 2 53 Ruspone of the Kingdom of Etruria, 6 174

VENICE.
Zechino or Sequin, shares in proportion, 26

WURTEMBERG.
Carolin, - - - - - 6 31
Ducat, - - - -

2 5
ZURICH.
Ducat, double and half in proportion, | 2 58

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SECTION LXXV.

GEOMETRY.

DEFINITIONS.

1. A point is that which has position, but no magnitude nor dimensions ; neither length, breadth, nor thickness.

2. A line is length, without breadth or thickness.

3. A surface or superficies is an extension, or a figure of two dimensions, length and breadth, but without thickness.

4. A body or solid is a figure of three dimensions ; viz. length, breadth, and thickness.

5. Lines are either right or curved, or mixed of these two.

6. A right or straight line lies all in the same direction between its extremities, and is the shortest distance between two points. When a line is mentioned simply, it means a right line.

7. A curve continually changes its direction between its extreme points.

8. Lines are either parallel, oblique, perpendicular, or tangential.

9. Parallel lines are always at the same perpendicular distance, and never meet, though ever so far produced.

10. Oblique lines change their distance from each other, and would meet if produced on the side of the least distance.

11. One line is perpendicular to another, when it inclines not more on the one side than the other, or when the angles on both sides of it are equal.

12. An angle is the inclination, or opening of two lines having different directions, and meeting in a point.

13. Angles are right or oblique, acute or obtuse.

14. A right angle is that which is made by one line perpendicular to another; or, when the angles on each side are equal to one another, they are right angles.

15. An oblique angle is one which is made by two oblique lines, and is either less or greater than a right angle.

16. An acute angle is less than a right angle.
17. An obtuse angle is greater than a right angle.
18. Superficies are either plane or curved.

19. A plane superficies, or plane, is that with which a right line may every way coincide; or, if the line touch the plane in two points, it will touch it in every point; but if not, it is curved.

20. Plane figures are bounded either by right lines or curves.

21. Plane figures, that are bounded by right lines, have names according to the number of their sides, or of their angles; for they have as many sides as angles, the least number being three.

22. A figure of three sides and angles is called a triangle; and it receives particular denominations from the relations of its sides and angles.

23. An equilateral triangle is that whose three sides are equal.

24. An isosceles triangle is that which has two sides equal.

25. A scalene triangle is that whose three sides are unequal.

26. A right-angled triangle is that which has one right angle.

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