About this book
Page.
Given the dimensions and content of any vessel, to find the
dimensions of a similar vessel of a given content ......... 23
PART II.
The Description and Use of the Sliding Rule.
The description of the sliding rule........................................................................ ........................... 24
To estimate the value of the divisions on the sliding rule......... 28
The use of the sliding rule ...........................................
Multiplication by the sliding rule...........................
Division by the sliding rule..........................................
Rule of Three .........
Inverse Proportion
33
To reduce a vulgar fraction to a decimal .......................... 35
Given a divisor to find a multiplier ................................................... 36
Given a multiplier to find a divisor.........
To square any number..................................................................................................
To extract the square root of any number............................................................................. 37
To find a mean proportional between two numbers......................... 38
To cube any number
To extract the cube root of any number.......
38
To erect a perpendicular upon a given line ................................................. 49
To let fall a perpendicular from a given point
To find the centre of a given circle ...
50
51
To construct a triangle with three given lines......
Given the base and perpendicular to construct a triangle........ 51
To describe a square whose side shall be equal to a given line... 52
To describe a rectangle whose length and breadth shall be equal
to two given lines ............................................................................... 52
........ 53
To construct a regular rhombus..........
To-construct an irregular rhombus............................................................................................ 53
To construct a regular rhomboid
54
To construct an irregular rhomboid .......................................................... 54
To construct an ellipse.................
To construct a regular pentagon...............................
To construct a regular hexagon
............ 55
To construct a regular octagon ....................................................................................................... 57
In a given triangle, to inscribe a circle ............................... ................ ............................. 57
About a given triangle, to circumscribe a circle .................. 58
To make a triangle equal to a given trapezium.................... 58
To make a right angle by the line of chords on the plane scale 59
To make an acute angle .......................................................................................................... 59
To make an obtuse angle..................................................
To find the number of degrees contained in any given angle ... 60
To make a regular polygon of any number of sides............... 60
In a given circle, to inscribe a regular polygon..................... 61
To raise a perpendicular by a scale of equal parts............................... 61.
To find the centre of a given ellipse ..........
To determine whether a given oval figure be greater or less than
a true ellipse....................................................................
...... 63
Geometrical Problems for the exercise of the Learner............ 64
Geometrical Theorems ............................................................................................................. 65
PART IV.
Mensurations of Superficies applied to Gauging.
Preliminary Observations
.... 71
Tables of ale and beer measure, 36 gallons to a barrel............ 72
Tables of ale and beer measure, 34 gallons to a barrel............ 73
Tables of ale and beer measure, 32 gallóns to a barrel............ 74
Tables of wine and spirit measure ...................................................................................
Tables of corn or dry measure.........
Tables of avoirdupois weight
76
... 77
b
The method of finding multipliers, divisors, and gauge-points... 78
To find multipliers for squares www............................................................................. 80
To find multipliers for circles........................
To find divisors for circles...................... `ÄŸ...............
To find gauge points for squares................................ ....................................................... 82
To find gauge-points for circles .....................................
A Table of multipliers, divisors, and gauge-points, for squares
and circles........................................................................................................................................... 83
Problems in Practical Gauging
To find the area of a square in ale, wine, and mash-tun gallons,
and malt bushels.....
To find the area of a rectangle
To find the area of a rhombus or rhomboides.
To find the area of a triangle, when the base and perpendicular
are given......ÿÿÿÿÿ........................6`♥ÿÿí............
To find the area of a triangle, when the sides are given ......... 99
To find the area of a trapezium
To find the area of a trapezoid
......
........... 104
To find the area of an irregular polygon ........................... 107
To find the area of a regular polygon ........................................... ... 111
To find the area of a regular polygon, when the side only is
given
113
To find the diameter and circumference of a circle.............. 115
To find the area of the sector of a circle ........
.... 117
........... 119
..... 123
To find the area of the segment of a circle ........................ 125
To find the area of an ellipse......................................
To find the area of any curvilineal figure, by means of equi-
Definitions of the conic sections ......
General properties of the conic sections ......
159
To find the content of a cubical vessel, in ale and wine gallons,
and malt bushels .......
.......... 165
To find the content of a vessel in the form of a parallelopipedon 169
To find the content of a vessel in the form of a prism.......... 172
To find the content of a vessel in the form of a cylinder ...... 175
To find the content of a vessel in the form of a pyramid
To find the content of a vessel in the form of the frustum of a
pyramid............
...... 177
To find the content of a vessel in the form of a cone ........... 184
cone
To find the content of a vessel in the form of a prismoid ...... 190
To find the content of a vessel in the form of a sphere or globe 194
To find the content of a vessel in the form of the segment of
To find the content of a vessel in the form of the frustum or
zone of a sphere ....................................
To find the content of a vessel in the form of a prolate spheroid 201
To find the content of a vessel in the form of the middle frus-
tum of a prolate spheroid .................................... 203
To find the content of a vessel in the form of a parabolic spindle 205
tum of a parabolic spindle ....
To find the content of a vessel in the form of a parabolic conoid 209
parabolic conoid .............
211
To find the content of a circular vessel when its sides are a
To find the content of a circular vessel when its sides are much
curved, by taking five diameters at equal distances from
To find the content of a circular vessel, when its sides are very
much curved, by taking a competent number of equi
distant, parallel sections
215
217
To find the content of a cylindrical ungula, when the liquor
intersects the sides of the vessel, în an oblique direction 222
To find the content of a cylindrical ungula, when its base is
less than a semi-circle
To find the content of a cylindrical ungula, when its base is a
semi-circle....
224
226
To find the content of a pyramidical or prismoidal ungula, in
the form of a cuneus or wedge..........
To find the content of a conical ungula, when the liquor just
covers the bottom of a conical vessel, placed upon its
greater base ..........
less base
...
229
233
235
To find the content of a conical ungula, when the liquor inter-
sects the sides of the vessel, in an oblique direction 236
To find the content of an elliptic ungula, when the liquor covers
only part of the bottom of a conical vessel, placed upon
its greater base.....
.........
To find the content of an elliptic ungula, when the liquor
covers only part of the bottom of a conical vessel, placed
upon its less base
238
241
To find the content of a parabolic ungula
243
To find the content of a hyperbolic ungula.
....
245
To find the area of the hyperbolic section formed by the sur-
face of the liquor ......