xml:lang="en" lang="en" dir="ltr">
##### Views

Keep up to date with the latest news - subscribe to the Transcribe Bentham newsletter; Find a new page to transcribe in our list of Untranscribed Manuscripts

# JB/135/084/003

Completed

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.

---page break---

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

---page break---

Prob.
XXII
n. 373
p. 274

To
find
the superficies
of a
segment
of a
globe,
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.

Prob
XXIII.
n. 375
p. 276

To
find
the solidity
or content
of a
cube.

Rule

Multiply
the
square
of a
side
by the
side,
and
the
product
will
express
the
content.

---page break---

Prob
XXIV.
n. 376
p. 277

To
find
the
content
of a
prism

Rule

Multiply
the area
of
the
base
by the
height
or
altitude
and
the
product
will
express
the
content.

---page break---

Prob.
XXV.
n. 377
p. 280

To
find
the
content
of a
wall
in
square
rods
of a
brick
and
half
thick

Rule

Multiply
the
area
of the
wall
in feet
by
the
number
of
half
bricks
in
thickness,
& divide
the
product
by 816
and
the
quotient
will
express
the
content
required

---page break---

Prob
XXVI
n. 378
p. 281

To find
the
content
of a
pyramid.

Rule

Multiply
the
area
of the
base
by a
third
part
of the
altitude,
and
the
product
will
give
the
content

---page break---

Prob
XXVII
n. 379
p. 282

To
find
the
content
of a
wedge
which
is a
solid
contained
under
five
plains
the
back
or base
is a
rectangle
or
oblong
and
the
four
sides
terminate
in
the
edge
E.F.
being
a strait
line
parallel &
equal
to a
side
of the
base.

Rule

Multiply
the
area
of the
base
by
half
the
altitude
of the edge.
and
the
product
will
give
the
content

---page break---

Prob.
XXVIII
n. 380
p. 283

To
find
the
content
of
a pavilion
roof
which
is a
solid
contained
under
five
plains
the base
is a
rectangle
or oblong
and
the
four
sides
terminate
in a
ridge
parallel
to
a side
of the
base,
but
unequal
to it.

Rule

To the
length
of the
ridge
twice
the
side
of the
base
which
is parallel
to it.
Multiply
the
sum
by the
other
side
of the
base,
and
the
product
which
arises
by a
sixth
part
of the
altitude,
and the
second
product
will
give ye
content

---page break---

Prob.
XXIX
n. 381
p. 284

To find
the
content
of the
frustum
of a
square
pyramid,
by a
section
parallel
to the
base

Rule

To the
areas
of the
ends
the
product
of their
sides,
multiply
the
sum
by a
third
part
of the
altitude
and
the
product
will
give
the
content.

---page break---

Prob.
XXX
n 382
p. 285

To
find
the
content
of
a prismoid
being
a solid
contained
under
six
plains
the bases
or
end
are
parallel
rectangles
or oblongs
and
the
four
sides
are

Rule

To the
areas
of the
ends
the
product
of the
sums
of their
lengths
and multiply
this
sum
by a
sixth
part
of the
altitude
and
the
product
will
give
the
content.

---page break---

Prob.
XXXI
n. 383
p. 286

To
find
the
content
of a
cylinder.

Rule

Multiply
the
area
of the
base
by the
altitude
of the
cylinder,
and
the
product
will
express
the
content.

---page break---

Prob.
XXXII
n. 384
p. 287

To find
the
content
of a
triangular
cestern,
whose
bottom
is the
sector
of a
circle.

Rule

Multiply
the area
of the
bottom
in inches,
by the
depth
in inches;
divide
the
product
by 282
and
the
quotient
will
be the
content
in gallons.

---page break---

Prob.
XXXIII
n. 385
p. 288

The bung
diameter,
diameter,
and
length
of a
(within
side)
being
given:
to find
the
content
of
a cylinder
nearly
equal
to it:
which
is called
gaughing
the

Rule

To the
diameter,
seven
tenth
parts
of the
difference
between
the
bung
diameters,
and
the
sum
will be
a mean
diameter
of
the
or the
diameter
of
a cylinder
equal
to the
Multiply
the
square
of the
mean
diameter,
the
length
of the
and 0,78
together,
and
the product will be the content, nearly

---page break---

Prob.
XXXIV
n. 386
p. 289

To
find
the
content
of a
cone.

Rule.

Multiply
the
area
of the
base
by a
third
part
of the
altitude,
and
the
product
will
give
the
content.

---page break---

Prob.
XXXV
n. 387
p. 290

To
find
the
content
of the
frustum
of a
cone
by a
section
parallel
to
the
base.

Rule

To the
squares
of the
diameters
circumferences
of the
ends
their
product;
multiply
the
sum
by the
altitude
of the
frustum,
and
the
product
which
arises
by 0,2618
0,0268
and
this
last
product
will
give
the
content.

---page break---

Prob
XXXVI
n. 388
p. 292

To
measure
timber.

Rule

Multiply
the
square
of the
girt
in inches
by the
length
in feet
divide
the
product
by 144,
and
the
quotient
will
give
the
content
in
feet.

---page break---

Prob
XXXVII
n 389
p 294

The
diameter
of a
globe
being
given,
to find
the solidity,
or
content.

Rules

1. Find
the
superficies
by the
373,
multiply
the
superficies
by a
third
part
of the
semidiameter,
the
product
will
give
the
content.
2. Find
the
content
of a
circumscribing
cylinder
by
the 383
and
take
two
thirds
of it
for the
content
of the
globe.

---page break---

Prob.
XXXVII
n 390
p. 295

The
diameter
of
a globe
being
given,
to find
the
content.

Rule.

Multiply
the
cube
of the
diameter
by
0,5236
and
the
product
will
give
the
content.

---page break---

Prob.
XXXVIII.
n. 391
p. 296

To
find
the
content
of a
segment
of a
globe
by the
section
of a
plain.

Rule.

From
three
times
the diameter
of
the
globe
take
twice
the
altitude
of the
segment;
multiply
together
the
remainder,
the
square
of the
altitude,
& 0,5236
and
this
product
will
give
the
content.

---page break---

A Table shewing
the weight of a cubic
foot, of various bodies,
in pounds averdupoise.

lb oz
Gold ... 1227 8
Quicksilver ... 860 2
Silver ... 693 3
Copper ... 548 1
Steel ... 490 10
Bar-iron ... 485 4
Block tin ... 452 6
Cast iron ... 445 15
Marble ... 169 6
Portland Stone ... 160 10
Free Stone ... 147 —
Loom ... 135 —
Brick ... 125 —
Gravel ... 109 5
Clay ... 107 0
Chalk ... 67 7
Salt Water ... 64 6
Rain Water ... 62 8
Salt ... 43 12
Mahogany ... 66 7
Oak ... 57 8
Beech ... 53 6
Ash ... 50 —
Yellow fir ... 41 1
Walnut ... 39 7
Elm ... 37 8
White deal ... 35 9
Pease ... 50 8
Beans ... 50 7
Wheat ... 48 4
Barley ... 41 2
Malt ... 30 5
Oats ... 29 8

Identifier: | JB/135/084/003
"JB/" can not be assigned to a declared number type with value 135.

135

posology

084

geometry - iv

003

copy/fair copy sheet

recto

46202