Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

The folid Content of the Fruftum is $497-79; and, if the Cone that was cut off is measured, (whofe Diameter at the Bafe BC is 10, and perpendicular Height 30, found by fubtracting the Height of the Fruftum from the Height of the Cone) the Content will be found 785.4, which being added to the Content of the Fruftum is 6283.19, which is the Content of the whole Cone within less than one hundredth Part; and even that Difference is owing to the Defect in taking the third Part of the Square of the Difference of the Bases.

Article 83. To meafure a Pyramid.

Definition. A Pyramid is a Solid, which, from a triangular or other figured Bafe, leffens regularly 'till it ends in a Point. Rule. Find the Area of the Bafe, whether a Triangle, Square, Heptagon, or the like, by the Rules laid down in Superficial Measure; then multiplying the Area of the Base by one Third of the Height, that Product is the folid Content of the Pyramid.

Exam. 1. A quadrangular Pyramid, the Height BE being 75, and each Side of the Bafe 18, to find the Content?

B

[blocks in formation]

Exam. 2. A triangular Pyramid, the Height BE being 96, and each Side of the Base 25; and the Bafe of this Figure being a Triangle, let the perpendicular Height DE be 21.65; to find the Content?

21.65 Per

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small]

Article 84. To measure the Fruftum of a Pyramid. Definition, The Fruftum of a Pyramid is what remains after the Top is cut off by a Plane parallel to the Base.

Rule. Multiply the Side of the greater Bafe by the Side of the leffer, and to the Product add one Third of the Square of the Difference of the Sides: If it is a quadrangular Bafe, this is the mean Area between the Bafes; but, if the Bafe is any other regular Figure, take the Multiplier in the Table, Art. 60, by which multiplying this Sum, the Product is the mean Area between the Bafes: Laftly, multiplying this by the Height, it gives the Content of the Fruftum.

[ocr errors]

Exam. 1. The Side of the greater Bafe AD 18, as before, the Side of the leffer BC 6, and the Height EF 50, to find the Content?

156
50

[blocks in formation]
[blocks in formation]
[blocks in formation]
[blocks in formation]

D

156

144 Square of the Difference.

48 of the Square.

Exam. 2.

Exam. 2. The Side of the greater Base AC 25, as before, the Side of the leffer Base BD 12.5, and the Height EF 48, to find the Content ?

12.5
25

[blocks in formation]

25

12.5

[blocks in formation]

When one Third of the Square of the Difference is added to the Rectangle of the Sides of the Bafes, multiply by 433, the tabular Multiplier for Triangles, Art. 60, which gives 157.86, the other Decimals being cut off to fhorten the Work; only, in multiplying, remember to add what is to be carried, that is, 2 when you multiply by 8, for 8 times 3 is 24, and I when you multiply by 4, for 4 times 3 is 12.

If the Pyramids that were cut off are meafured, by Art. 83, and their Content added to the Content of their respective

Fruftums,

Fruftums, they will be the fame as the Content found in that Article, abating what may be loft in retrenching the Decimals. The Bafes of thefe Pyramids are the fame with the lefler Bafes of the Fruftums: The Height of the triangular Pyramid that was cut off is 48, and the Height of the quadrangular 25, found as at Art. 82: The Area of the firft will be found 1082.5, and of the other 300, which the Learner may try for his Exercife and Improvement.

Article 85. To measure a Globe.

Definition. A Globe is a round folid Body, in the Middle of which is a Point, from which all Lines drawn to the Surface are equal,

Rule. Cube the Diameter, then multiply that Cube by .5236, and the Product is the folid Content of the Globe.

Exam. The Diameter of a Globe is 3 2, to find the Content?

[blocks in formation]

If the Circumference of the Globe is given, cube the Circumference, and multiply the Cube by .016887 for the Content.

Article

[ocr errors]

Article 86. To measure the Surface of a Globe.

Rule. Multiply the Circumference and Diameter together, and the Product is the fuperficial Content, or Area, of the Surface of the Globe.

Exam. The Diameter of a Globe being 3.2, to find its Area?

[blocks in formation]

Article 87. To meafure the Solidity of a Fruftum or Segment of a Globe.

Definition. The Fruftum of a Globe is any Part cut off by a Plane.

Rule. To three times the Square of the Semidiameter of the Bafe add the Square of the Height; then multiplying that Sum by the Height, and the Product by .5236, it gives the folid Content.

Exam. The Height BD being 12 Inches, and the Diameter of the Base AC 26 Inches, to find the Content?

[blocks in formation]

4090.3632 folid Content,

Article

« ΠροηγούμενηΣυνέχεια »