Arithmetic, Part 1 · Section 41 – Section 42

Arithmetic · Part 1 · Section 41 – Section 42

p. 1672 Cent.

3 Cent.

4 Cent.

5 Cent.

6 Cent.

7 Cent.

8 Cent.

p. 1759 Cent.

p. 177Some uſes of the Square and Cube Root.

Uſes of the Square Root.

WHat the Square and Cube Roots are, and how to extract them, hath already been taght, and for more eaſe and expedition, there are Tables ready calculated, both of the Square and Cube Roots, from 1 to 1000, we come now to ſhew ſome uſes thereof, which in ſome meaſure will appear in the Propoſitions following.

PROPOSITION. I.

Admit the height of the Wall of a Fort or Caſtle to be ſcaled, be 30 foot, and the breadth of the Trench about the Fort be 40 foot, I demand of what length a Scaling Ladder ſhould be, juſtly to reach from the edge of the Trench, to the top of the Wall.

By the 47th. of the firſt Book of Euclides Elements, it is demonſtrated that the ſquare of the Hypotenuſal of all right angled plain Triangles is equal to the ſquares of the 2 other ſides; I therefore to reſolve this Propoſition, ſquare the height of the Wall which is 30, facit 900, alſo I ſquare the breadth of the Trench which is 40, facit 1600, theſe two added together make 2500, the ſquare root whereof is 50, and ſo long muſt Scaling Ladders be made to reach from the edge of the Trench to the top of the Wall.

p. 178PROPOSITION II.

There be two Towns, as Chicheſter and York, which lie North and South one from another, and their diſtance is 220 miles, and Exceſter lieth directly Weſt from Chicheſter 120 miles; I deſire to know the diſtance of York from Exceſter.

Square 120,

Exceſter

120

Chicheſter

220

York

the diſtance of Exceſter and Chicheſter, it maketh 14400, likewiſe ſquare 220, the diſtance of York and Chicheſter, facit 48400, theſe two numbers added together make 62800, whoſe ſquare root extracted (or found in the Tables) will be 250 3/5; neer, and ſo many miles is Exceſter diſtant from York.

Ʋſe of the Cube Root.

ONe chief uſe of the Cube Root, is to find out a proportion between, like Solids, ſuch are Spheres, Cubes, and ſuch like; as in the Propoſion following.

PROPOSITION.

If a Bullet of Braſſe of 4 inches Diameter, weigh 9 pound, what ſhall a Bullet of Braſſe weigh, whoſe Diameter is 8 inches?

Cube 4 the Diameter of the leſſer Bullet, makes 64, likewiſe Cube the Diameter of the greater Bullet 8, makes 4608. This done, ſay by the Rule of proportion; If the Cube number 6…, give 9 li. weight, what ſhall the Cube number 4608 give? Multiply and divide, you ſhall find 72, and ſo many pounds will a Bullet of Braſſe weigh, whoſe Diameter is 8 inches.