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Prob.
I.
n. 343
p. 246
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 (as
you go
on) place
the first
remainder
under
the
multiplying
figure,
and the
rest in
order,
adding
the several
quotients
to
the next
arising
products;
and
having
thus
finished
the
multiplication,
the
sum of
all will
be the
product
required.
Prob.
II.
n. 344
p. 247
To
find
the area,
or content
of a
square.
Rule
Multiply
the
length
of the
side
by itself,
and
the
product
will
express
the area.
Prob.
III.
n. 345
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.
Prob.
IV
n. 346
p. 250
To
find
the area
of a
parallelogram
Rule
Multiply
the length
by the
breadth
and
the
product
will
give
the
area.
Prob.
V.
n. 348
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
and
the
product
will
give
the
area.
Prob.
VI.
N. 349
p. 253
To
find
the
area
of a
triangle.
Rule:
1. Multiply
the base
by half
the altitude
or the
altitude
by
half
the
base,
and
the
product
gives
the
area.
Or —
2. Half
the
product
of the
base
and
altitude
will
give
the
area.
Prob
VII.
n. 350
p. 254
To
find
the
area
of
any
quadrangle.
Rule.
Measure
a diagonal
line,
and
the perpendicular
falling
upon
it from
the
opposite
Angles;
multiply
the
sum
of
these
perpendiculars
by half
the
diagonal,
and
the
product
will
give
the area,
or multiply
the
sum
of the
perpendiculars
by the
diagonal,
and
half
the
product
will
give
the
area.
Prob.
VIII.
n. 351
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.
VI.
and
their
sum
will
be the
content.
Or —
2. Make
a triangle
equal
to the
given
figure
by
article
312,
and
find
the
area
of this
equal
triangle.
Prob.
IX
n. 352
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.
Prob
X.
n. 353
p. 257
To
find
the
circumference
of a
circle
whose
diameter
is 2.
Prob.
XI.
n. 361
p. 260
To
find
the
area
of a
circle
whose
diameter
and
circumference
are
given.
Rules
Multiply
half
the
circumference,
by half
the
diameter,
and
the
product
will
express
the area.
Or
Multiply
the
circumference
by the
diameter,
and
a fourth
part
of the
product
will
express
the
area.
Prob.
XII
n. 362
p 261
The diameter
or semidiameter
of a
circle
being
given
to find
the area
of that
circle.
Rules
1. Multiply
the
square
of the
diameter
by 0,7854,
and
the
product
will
give
the
area.
Or
2. Multiply
the
square
of the
semidiameter
by 3,1416 &
the
product
will
give
the
area.
Prob.XIII
n. 363
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
and
the
product
will
give
the
area.
Prob.
XIV
n. 364
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,
and
the
product
will
express
the
area.
Prob
XV
n. 365
p. 265
To
find
the
area
of a
segment
of a
sector
or the
front
of an
arch
built
with
stone
of
equal
length
Rule.
Multiply
half
the
sum
of the
bounding
arches
by their
distance
and
the
product
will
give
the
area
Prob
XVI
n. 366
p. 267
To
find
the area
of a
segment
of a
circle
whose
center
is E
Rules
Find
the
area
of the
triangle
A, B, E,
and of
the
sector
A.C.B.
E. by
articles
349
364
and their
difference
is the
area
of the
segment
or
2. 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.
Prob
XVII
n. 367
p. 268
To
find
the
area
of an
ellipsis,
or oval.
Rule
Multiply
0,7854
the
greatest
diameter
and
the
least
diameter
together,
and
the
product
of
these
three
numbers
will
express
the
area.
Prob.
XVIII
n. 368
p 269
To
find
the
convex
surface
of a
right
cylinder.
Rule
Multiply
the
circumference
of the
base
by the
altitude
of the
cylinder,
and
the
product
will
give
the
convex
surface.
Prob
XIX.
n. 369
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
area.
Prob
XX
n. 370
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
circumferences
of the
ends
by the
slant
side;
and
the
product
will
give
the
convex
surface.
Prob.
XXI
n. 371
p. 272
The
diameter
of a
globe
being
given,
to find
the
superficies.
Rule
Find
the
circumference
of a
great
circle
upon
the
globe
by
article
356
multiply
the
circumference
by the
diameter,
and
the
product
will
express
the
superficies.
Prob.
XXI
n. 372
p. 273
The
diameter
or semidiameter
of
a globe
being
given,
to find
the
superficies.
Rules
Multiply
3,1416
by the
square
of the
diameter &
the
product
will
give
the
superficies.
or
2. Multiply
the
square
of the
semidiameter
by 88
divide
the
product
by 7,
and
the
quotient
will
give
the
superficies
Prob.
XXII
n. 373
p. 274
To
find
the superficies
of a
segment
of a
globe,
made
by the
section
of a
plain
Rule
Multiply
the
circumference
of the
globe
by the
height
of the
segment
and
the
product
will
give
the
superficies.
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geometry - iv |
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