The English academy, or, A brief introduction to the seven liberal arts grammar, arithmetick, geometrie, musick, astronomie, rhetorick & logic : to which is added the necessary arts and mysteries of navigation, dyaling, surveying, mensuration, gauging & fortification, practically laid down in all their material points and particulars, highly approved to be known by the ingenious, and as such are desirous to profit, or render themselves accomplished : chiefly intended for the instruction of young scholars, who are acquainted with no other than their native language, but may also be very useful to other persons that have made some progress in the studies of the said arts / by John Newton.

CHAP. IV. Of Bodies or Solids.

AFter the description of lines and planes, the Doctrine of Bodies is to be consi∣dered.

2. A Solid or Body, is that which hath Length, Breadth and Thickness, whose bounds or limits are Superficies.

3. A Solid is either Plane or Gibbous.

4. A Plane Solid, is that which is compre∣hended of Plane Superfices, and is either a Pyramide or Pyramidate.

5. A Pyramide, is a solid Figure, which is contained by Planes, set upon one Plane or Base, and meeting in one point.

6. A Pyramidate, is a solid Figure, com∣posed of Pyramides, and is either a Prisme or a mixt Polyhedron.

7. A Prisme, is a Pyramidate or solid Fi∣gure, by Planes, of which these two which are opposite, are equal, like, and parallel and all the other Planes are parallelograms.

8. A Prisme, is either a Pentahedron, a Hexahedron, or a Polyhedron.

9. A Pentahedron Prisme, is that, which comprehended of five sides, and the Base Triangle.

10. An Hexahedren Prisme, is that which is comprehended of six sides, and the Base a Quadrangle.

11. An Hexahedron Prisme, is either a Parallelipipedon, or a Trapezium.

12. A Parallelipipedon, is that whose sides or opposite planes are parallelograms.

13. A Prisme, called otherwise a Trapezi∣um, is that solid, whose opposite planes or sides are neither parallel nor equal.

14. A Parallelipipedon, is either Right an∣gled or Oblique.

15. A Right angled Parallelipipedon, is that which is comprehended of right angled sides and it is either a Cube or an Oblong.

16. A Cube, is a Right angled parallelipi∣pedon of equal sides.

17. An Oblong, is a right angled paralleli∣pipedon of unequal sides.

18. An Oblique angled Parallelipipedon, is that which is comprehended of oblique sides

19. A Polyhedron, is that which is compre∣hended of more than five sides, and the Base a Multangle.

20. A mixt Polyhedron, is that whose Ver∣tex is in the Centre, and the several sides exposed to view, and of this sort, there are only three; the Octahedron, the Icosohedron, and the Dodecahedron.

21. An Octahedron, is a solid Figure, which is contained by eight Equal and Equilateral Triangles.

22. An Icosohedron, is a solid Figure, which is contained by twenty Equal and Equilate∣ral Triangles.

23. A Dodecahedron, is a solid Figure, which is contained by twelve Pentagons, E∣quilateral and Equiangled.

24. A Gibbous solid, is that which is com∣prehended of Gibbous Superficies, and it is either a Sphere or Various.

25. A Sphere, is a Gibbous body, abso∣lutely Round and Globular.

26. A Various Gibbous Body, is that which is comprehended by various superficies and a circular base; and is either a Cone, or a Cylinder.

27. A Cone, is a Pyramidical Body, whose Base is a Circle.

28. A Cylinder, is a solid Body of equal thickness, having a Circle for its Base. The solid content of these several Bodies may be measured by the Problems following.

Problem I. The Base and Altitude of a Pyramide or Cone given, to find the Solid Content.

Multiply the Altitude by a third part of the Base, or the whole Base by a third part of the Altitude, the Product shall be the so∣lid Content required.

Problem II. The Base of a Prisme or Cylinder being gi∣ven, to find the sold content.

Multiply the Base of the Prisme or Cylin∣der given, by the Altitude, the Product shall be the solid content.

Problem III. In a Piece or Frustum of a Pyramide, Cone or other irregular Solid, both the bases being gi∣ven, to find the content.

If the Aggregate of both the Bases of the Frustum, and of the mean Proportional be∣tween them, be drawn into the Altitude of the Frustum, the third part of the Product shall be equal to the solid content required.

Problem IV. The Axis of a Sphere being given, to find the solid content.

A Sphere (as Archimedes hath shewed) is equal to two thirds of a Cylinder circum∣scribing it; now then, such a Cylinder be∣ing made; by the Area of a Circle multi∣plyed by the Diameter; and therefore the

Area of a Circle being multiplied by two thirds of the Diameter, the Product shall be the solid content of a Sphere.

The Area of a Circle whose Diameter is 1, is 7853975, which being multiplied by 666666, the two thirds of the Diameter, the Product 523598 is the solid content of such a Sphere; therefore,

As 1 to 523598, so is the Cube of any Ax∣is given, to the solid content required.

FINIS.