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No 343. Prob. 1. p.
To multiply feet, inches
& parts, by feet, inches, &
parts, which method is
termed cross multiplication.
Rule
Set the feet in the multiplier
under the least denomination
in the multiplicand,
and the rest in
order; multiply as in
common arithmetick,
divide each product by
12, place the first remainder
under the multiplying
figure, adding the several
quotients to the next arising products; and ye sum of all will be the prod. req.
No 344. Prob. 2. p. 24
To find the area, or
content of a square.
Rule.
Multiply the length
of the side by itself, &
the product will express
the area.
No 345. Prob. 3. p 248
To find the area of
a rectangle or oblong
Rule.
Multiply the length
by the breadth, namely,
the base by the perpendicular;
and the product
will express the area
No 346 Prob. 4. p. 250.
To find the area of a
parallelogram.
Rule.
Multiply the length by
the breadth.
No 348. Prob. 5. p. 252
To find the area of a
quadrangle, having two
parallel sides.
Rule.
Multiply half the sum
of the parallel sides by
the perpendicular between
them.
No 349. Prob. 6. p. 253
To find the area of a
triangle.
Rules
1. Multiply the base by
half the altitude, or the
altitude by half the base
Or. 2. Half the product
of the base and altitude
will give the area.
No. 350. Prob. 7. p. 254
To find the area of any
quadrangle.
Measure a diagonal
line and the perpendiculars
falling upon it
from the opposite angles;
and multiply the sum
of the perpendiculars
by half the diagonal;
or, multiply the sum
of the perpendiculars
by the diagonal, and
half the product will
give the area.
No 351. Prob. 8. p 255
To find the area of any
strait lined figure.
Rules.
1. Divide the figure
into triangles, find
the area of each triangle
by Prob. 6, and their
sum will be the content.
Or
2. Make a triangle equal
to the given figure
and find the area of
this equal triangle.
No 352 Prob. 9. p. 256
To find the area of any
regular polygon.
Rule.
Let fall a perpendicular
from the center of
the figure to one of its
sides; then multiply
together the perpendicular,
the side of the
figure, and the number
of its sides; and
half the product will
express the area.
No 353. Prob. 10 p. 257
To find the circumference
of a circle whose
diameter is 2.given.
Rule
Multiply the diameter
by 3,1416.
No 361 Prob. 11 p. 260
To find the area of a
circle, whose diameter
and circumference are
given.
Rules
Multiply half the
circumference by half
the diameter. Or
Multiply the circumference
by the diameter
and a fourth part
of the product will express
the area.
No 362. Prob. 12. p 261
The diameter, or semidiameter
of a circle
being given, to find
the area of that circle.
1. Multiply the square
of the diameter by 0,7854. Or
2. Multiply the square
of the semidiameter
by 3,1416.
No 363 Prob. 13. p 263
The circumference of a
circle being given, to
find the area.
Rules
1. Find the semidiameter
by the 360, and
then find the area by
the 361. Or
2. Multiply the square
of the circumference by
0,079577.
No 364. Prob. 14. p 264
To find the area of a
sector of a circle.
Rule
Multiply the length of
the arch by the radius
of the circle, and half
the product will give
the area. Or multiply
either of them by half
the other.
No 365. Prob. 15. p. 265
To find the area of a
segment of a sector,
or the front of an arch
built with stones of equal
length.
Rule.
Multiply half the
sum of the bounding
arches by their distance.
No 366. Prob. 16. p. 267
To find the area of a
segment of a circle.
Rules
To six times the base,
add eight times the
chord of half the arch,
multiply the sum by
the altitude, divide the
product by 15, and the
quotient will nearly give
the area. Or
No 367. Prob. 17. p. 260
To find the area of an
ellipsis, or oval.
Rule
Multiply 0,7854, the
greatest diameter, &
the least diameter together.
No 368 Prob. 18. p 269
To find the convex
surface of a right cylinder.
Rule.
Multiply the circumference
of the base by
the altitude of the cylinder.
No 369. Prob. 19. p. 270
To find the convex
surface of a right cone.
Rule.
Multiply the circumference
of the base by
the slant side, and
half the product will
give the convex surface.
No 370. Prob. 20. p. 271.
To find the convex surface
of the frustum
of a right cone, made
by a section parallel
to the base
Rule.
Multiply half the
sum of the circumference
of the ends by
the slant side.
No 371 Prob. 21
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