PROP. 23.To shew that the G.C.M. of several numbers may be obtained
by finding first the G.C.M. of two, then of this and a third, next
of this last and a fourth, and so on; the last so obtained being the
G.C.M. of the whole
138
PROP. 24.–To prove the Rule for finding the L.C.M. of several numbers 139
PROP. 25.To shew that the L.C.M. of three or more numbers may be
obtained, by finding first the L.C.M. of two, then of this and a third ;
next of this last and a fourth, and so on; the L.C.M. last found being
that required
140
PROP. 26.—To explain the necessity, method, and meaning of the system
of Fractional Numeration and Notation
PROP. 27.The numerator and denominator of a fraction may be both
multiplied or divided by any the same number, without altering its
value
143
PROP. 28.—To prove the Rule for reducing fractions to their L.C.D. 144
PROP. 29.To explain the Rule for Addition of fractions
144
PROP. 30.To explain the Rule for Subtraction of fractions
145
PROP. 31.—To prove the Rule for Multiplication of a fraction by an
integer .
145
PROP. 32.—To prove the Rule for division of a fraction by an integer 146
PROP. 33.—To prove the Rule for finding the value of a compound
fraction
146
PROP. 34.To explain the meaning of the Multiplication by a fraction,
and to deduce a Rule for finding the product
147
PROP. 35.—To explain the meaning of Division by a fraction, and to de
duce a Rule for forming the quotient
149
PROP. 36.To explain the meaning of a complex fraction, and to deduce
a Rule for its reduction to a simple fraction
150
PROP. 37.To explain the system of notation of decimal fractions 152
PROP. 38.To explain the Rules for Addition and Subtraction of decimals 153
PROP. 39.—To prove the Rule for Multiplication of a Decimal by any
power of 10
154
PROP. 40.To prove the Rule for Division of a Decimal by any power
of 10

154
PROP. 41. To prove the Rule for Multiplication of Decimals
154
PROP. 42.–To prove the Rule for Division of Decimals
155
PROP. 43.To shew under what circumstances a vulgar fraction is con
vertible into a finite decimal; and that, in all cases, where the deci
mal is infinite, the figures recur in a certain order; and to find the
extent of the recurring period
155
PROP. 44.To prove the Rule for the conversion of a recurring decimal
into a vulgar fraction
157
PROP. 45.To shew that the ratio of one number or quantity to another
may be properly represented by the fraction, whose numerator is the
number of units in the former, and denominator the number of the
same kind of units in the latter, quantity
158
PROP. 46.To shew how to divide a number or quantity into parts, which
shall bear to each other a given ratio
159
PROP. 47.—To shew that if four numbers be proportional in a given
order, the product of the extremes is equal to that of the means, and
conversely
159
PROP. 48.—To find a fourth proportional to three given numbers
160
PROP. 49.To find a third proportional to two given numbers
160
Prop. 50.—To find a mean proportional to two given numbers
161
PROP. 51.To shew that, if the corresponding terms of any number of
proportions be multiplied together, they will still form á proportion 161
b