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PROD.
Definition
Notation
Decimal Fractions.
I. To add decimals together
II. To subtract one decimal from another
III. To multiply decimals
IV. To divide decimals
V. To reduce a vulgar fraction to a decimal one
VI. To reduce the known parts of any integer to
decimal fraction
VII. To reduce a decimal to the known parts of
integer
Duodecimals.
IX. To raise a given number to any given power re-
quired
137
. 138
139
I. To find the area of any parallelogram, whether
it be a square, a rectangle, a rhombus, or a
rhomboides
II. To find the area of a triangle
III.
To find the area of a triangle, the three sides
being given
IV. Any two sides of a right-angled triangle being
given, to find a third
V. To find the area of a trapezium
VI. To find the area of a trapezoid
154
1 156
157
159
1 163
. 163
VII. To find the area of any regular polygon
PROB.
PAGE
VIII. To find the area of any regular polygon when
the side only is given
IX. The diameter of a circle being given, to find the
circumference, or the circumference being
given, to find the diameter
X. The chord and height of any segment being given,
to find the chord of half the arc
165
167
-
169
XI. To find the length of any are of a circle, the
chord and height of the arc being given
170
XII. The chord and height of the segment being
given, to find the radius of the circle
XIII. Given any two parallel chords, and their dis-
tance, to find the distance of the greater
chord from the centre
171
172
XIV. Given a chord of a circle, and its distance from
the centre, to find the radius of the circle
173
XV. Given any two parallel chords in a circle, and
their distance between them, to find the per-
pendicular height from the middle of either
chord to the circumference
XVI. The diameter of a circle being given, to find
XVII. To find the area of the sector of a circle
XVIII. To find the area of the segment, the chord and height of the segment being given
XIX. To find the area of a circular zone, being that
part of a circle laying between two parallel
chords, and the parts of the circle intercepted
by the chords
177
181
PROE. •
XX. To find the diameter of a circle, whose area
shall be in a given proportion to the area of
a circle whose diameter is known
183
XXI. To find the circumference of an ellipsis, the.
transverse and conjugate axes being given
XXII. To find the area of an ellipsis, the transverse
and conjugate axes being given
184
185
XXIII. To find the area of a parabola, the base and
height being given
XXIV. To find the area of the frustum of a parabola,
the two parallel ends and their distance be-
tween being given
136
III. To find the solidity of the frustum of a pyramid 194
IV. To find the solidity of the frustum of a cone
196
Of a Prismoid.
I. To find the solidity of a prismoid
II. To find the solidity of a sphere or globe
III. To find the solidity of the segment of a globe
IV. To find the solidity of a spherical zone, the two
ends and their distance being given
FAGE
199
200
V. To find the solidity of a wedge
201
VI. To find the solidity of a hoof from the frustum
of a square pyramid
202
VII. To find the solidity of a spheroid, the fixed and
revolving axes being given
VIII. To find the solidity of a parabola conoid, the
diameter of the base and perpendicular height
IX. To find the solidity of the frustum of a parabola
conoid
203
Of an Annulus, or Cylindric Ring.
205
- 206
I. To find the solidity of an annulus, or ring
II. To find the solidity of a hollow cylinder
III. To find the solidity of the hollow frustum of a
IV. To find the solidity of the hollow segment of a
sphere
V. To find the solidity of the hollow frustum of a
Conver Surfaces of Solids.
I. To find the convex surface of a cylinder
II. To find the convex surface of a cone
209
210