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36. The units in the three systems when expressed in terms of one common standard, two right angles, stand thus :

the unit in the Sexagesimal Method =

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1

180

1

200

1

π

of two right angles,

of two right angles,

of two right angles.

37. It is not usual to assign any distinguishing mark to angles estimated by the Third Method, but for the purpose of stating the relation between the three units in a clear and concise form, we shall use the symbol 1o to express the unit of circular measure.

Then we express the relation between the units thus:

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CHAPTER III.

ON THE METHOD OF CONVERTING THE MEASURES OF ANGLES

FROM ONE TO ANOTHER SYSTEM OF MEASUREMENT.

38. WE proceed to explain the process for converting the measures of angles from each of the three systems of measurement described in Chap. II. to the other two.

39. To convert the measure of an angle expressed in degrees to the corresponding measure in grades.

Let the given angle contain D degrees.

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Hence we obtain the following rule: If an angle be expressed in degrees, multiply the measure in degrees by 10, divide the result by 9, and you obtain the measure of the angle in grades.

Ex. How many grades are contained in the angle 24°. 51′.45′′? 24°. 51′. 45′′ = 24.8625 degrees

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36. The units in the three systems when expressed in terms of one common standard, two right angles, stand thus:

the unit in the Sexagesimal Method =

the unit in the Centesimal Method

the unit in the Circular Method

=

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1

180

1

200

1

π

of two right angles,

of two right angles,

of two right angles.

37. It is not usual to assign any distinguishing mark to angles estimated by the Third Method, but for the purpose of stating the relation between the three units in a clear and concise form, we shall use the symbol 1° to express the unit of circular measure.

Then we express the relation between the units thus:

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CHAPTER III.

ON THE METHOD OF CONVERTING THE MEASURES OF ANGLES

FROM ONE TO ANOTHER SYSTEM OF MEASUREMENT.

38. WE proceed to explain the process for converting the measures of angles from each of the three systems of measurement described in Chap. II. to the other two.

39. To convert the measure of an angle expressed in degrees to the corresponding measure in grades.

Let the given angle contain D degrees.

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Hence we obtain the following rule: If an angle be expressed in degrees, multiply the measure in degrees by 10, divide the result by 9, and you obtain the measure of the angle in grades.

Ex. How many grades are contained in the angle 24°. 51'. 45′′? 24°. 51′. 45′′ = 24.8625 degrees.

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36. The units in the three systems when expressed in terms of one common standard, two right angles, stand thus:

the unit in the Sexagesimal Method =

the unit in the Centesimal Method

the unit in the Circular Method

=

=

1

180

1

200

1

=-
π

of two right angles,

of two right angles,

of two right angles.

37. It is not usual to assign any distinguishing mark to angles estimated by the Third Method, but for the purpose of stating the relation between the three units in a clear and concise form, we shall use the symbol 1° to express the unit of circular measure.

Then we express the relation between the units thus:

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