Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

Article 64. The Diameter being given, to find the Area of a Circle without finding the Circumference.

Rule. Square the Diameter, then multiply the Square by 78539, and the Product is the Area of the Circle whofe Diameter was given.

Exam, The Diameter of a Circle being 17, to find the Area?

[blocks in formation]

For greater Expedition, the Multiplier may be .7854, which will be fufficiently exact.

Article 65. The Circumference of a Circle being given, to find the Area without finding the Diameter.

Rule. Square the Circumference, then multiply that Square by .07958, and the Product is the Area of the Circle.

Exam. The Circumference of a Circle being 53.4, to find the Area?

[blocks in formation]

The Learner may perceive, that, in the three different Ways of finding the Area, the Differences are but small, tho' there was an Omiffion of fome of the Decimals to render the Work lefs tedious.

Article

Article 66. The Dimensions of any of the Parts of a Circle being given, to find the Side of a Square equal to the Circle.

Rule. If the Area of the Circle is given, extract the Square Root of the Area, which will be the Side of a Square equal to the Circle: If the Diameter or Circumference be given, find the Area by the Rules in Art. 64 or 65, and extract the Square Root of the Area found, which Root will be the Side of a Square equal to the given Circle. And this is a general Rule to find the Side of a Square equal to any fuperficial Figure, regular or irregular: For the Square Root of the Area of any Figure whatever is the Side of a Square equal to the given Figure. But, with Regard to Circles, if the Diameter is given, multiply it by .886, and the Product will be the Side of a Square equal to the Circle whofe Diameter was fo given And, if the Circumference is given, multiply it by .282, for the Side of a Square equal to the Circle whofe Circumference was fo multiplied.

[blocks in formation]

The Learner may try the Truth of thefe Operations, by finding whether the Area of a Circle whofe Diameter is 17 is the fame with the Area of the Square whofe Side is 15.062. The fecond Example may be tried in the fame Manner.

Article 67. The Area of a Circle being given, to find the Diameter.

Rule. Multiply the given Area by 1.2732, and the Product is the Square of the Diameter; then extracting the Square Root of the Product, you have the Diameter.

[ocr errors]

Exam. The Area of a Circle being 226.9, to find the

[blocks in formation]

Article 68. The Area of a Circle being given, to find the Circumference.

Rule. Multiply the given Area by 12.566, and extract the Square Root of the Product, which Root will be the Circumference of the Circle whofe Area was fo multiplied.

Exam. The Area of a Circle being 226.9, to find the Circumference?

2851.2254 (53.39 Circumference.

25

12.566

226.9

113094

103) 351

[blocks in formation]

In these two Examples, the Numbers come out fomewhat lefs than the Truth, but near enough for common Use.

Article

Article 69. The Side of a Square being given, to find the Diameter of a Circle equal to the Square whofe Side is given.

Rule. Multiply the given Side by 1.128, and the Product will be the Diameter of a Circle whofe Area is equal to the Area of the given Square.

Exam. The Side of a Square being 15.04, to find the Diameter of a Circle equal to that Square?

15.04
1.128

12032

3008

1504

1504

16.96512 Answer.

Article 70. The Side of a Square being given, to find the Circumference of a Circle equal to the given Square.

Rule. Multiply the given Side by 3.545, and the Product will be the Circumference of a Circle equal to the given Square. Exam. The Side of a Square being 15.04, to find the Circumference of a Circle equal to that Square?

15.04

3.545

7520

6016

7520

4512

53-31680 Anfwer.

The Truth of the Operations in the two laft Articles the Reader may try as at Art. 66.

Article 71. To find the Area of a Semicircle, the Diameter being given.

Rule. Find the Area of the Circle, by Art. 64, and take the Half of it.

In the fame Manner may the Area of a Quadrant, or a Quarter of a Circle, be found, by taking a fourth Part of the Area of the whole Circle.

But, with Regard to meafuring a Sector, or a Segment of a Circle, it will be neceffary first to fhew the Way to find the

· Length

Length of the Arch-Line of a Sector, and the Diameter of the Circle to a given Segment.

Article 72. A Sector or Segment of a Circle being given, to find the Length of the Arch-Line.

Rule. Divide the Segment into two equal Parts; then measure the Chord of the. Half-Arch, from the Double of which fubtract the Chord of the whole Segment; and one Third of that Difference, being added to the Double of the Chord of the Half-Arch, is the Length of the Arch-Line.

[blocks in formation]

Article 73. The Chord and verfed Sign of a Segment being given, to find the Diameter of a Circle.

Rule. Multiply Half the Chord by itself, and divide the Product by the verfed Sine; then add the Quotient to the verfed Sine, and the Sum is the Diameter of the Circle.

[merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
« ΠροηγούμενηΣυνέχεια »