The new method of fortification, as practised by Monsieur de Vauban, Engineer General of France with an explication of all terms appertaining to that art / made English.

PROBLEMS.

I. To turn a Cylinder into a Parallelepiped of the same height.

1. Instead of the Base of the Cylinder CBA, make a Square ABCD, by Prob. 23. Chap. 1. Book 1.

2. Raise upon ABCD four Perpendicu∣lars of the height of AB, which may repre∣sent

the height of the Cylinder, as EF GH.

3. Joyn EF, EH, FG, and GH toge∣ther by right lines; and you have the Pa∣rallelepiped.

II. To turn a Cone into a Pyramid of the same height.

1. Make a Triangle, Square, Pentagon, or what other Polygon you please, equal to the Base of the Cone CBD, and let it be the Base of a Pyramid, as ABCD.

2. Raise from the middle of the Base F a Perpendicular, of the height of the Cone BA, as FE; then draw from ABCD lines to the point, and the Pyramid is made.

III. To turn a Parallelepiped into a Cylinder.

Make a Circle equal to the Base of the Pa∣rallelepiped, and raise this Circle to be as high as the Parallelepiped, and the work is done.

IV. To turn a Pyramid into a Cone.

1. Make a Circle equal to the Base of the Pyramid.

2. Raise upon its Center a Perpendicular as high as the Pyramid, as BA.

3. Draw the extremities of the Diameter CD together till they meet at the top of the Perpendicular A, and the Cone will be finished.

V. To turn a Prism or a Cylinder into a Py∣ramid or a Cone of the same height, or the contrary.

1. Enlarge the Base of the Cylinder three times as much as it is, by Prob. 1. Chap. 2. Book 1.

2. Upon its Center raise a Perpendicular as high as the Cylinder, and draw the ex∣tremities of the Diameter together to the top of the Perpendicular, and the Pyramid will be made: In like manner you may turn a Cylinder or a Prism into a Cone: On the contrary, when you would make a Prism or a Cylinder equal to a Pyramid or a Cone, you must make the Base of the Py∣ramid or of the Cone three times less, and

then upon this Base erect a Cone or Pyra∣mid of the height of the Prism or Cylinder given.

VI. To make a Cube equal ta a Parallepiped.

1. If the Base of the Parallelepiped be square, find a mean proportional between its height and one side of the Base; this mean proportional will be the true mea∣sure of the Cube required.

2. If the Base be only a Parallelogram, turn it into a Square by Prob. 25. Chap. 2. Book 1. then go on as at first, and your work will be done.

VII. To make a Cube equal to a Cylinder given.

1. Make a Parallelepiped equal to a Cy∣linder given, by Problem 1. of this Chap∣ter.

2. Afterwards make a Cube equal to that Parallelepiped, by the precedent Problem, and you have the Cube desired.

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VIII. To make a Cube equal to a given Co••e.

1. Make a Parallelepiped equal to a gi∣ven Cone, by Problem 5•• of this Chap∣ter.

2. Afterwards make a Cube equal to that Parallelepiped by Problem 6. of this Chap∣ter.

IX. To make a Cube equal to a Pyramid.

This Problem must be wrought like the last foregoing.

X. To make a Cone equal to a Globe.

1. Take one of the great Circles of your Globe, and make it four times bigger, by Prob. 11. Book 1. Chap. 2.

2. Raise a Cone upon this Base as high as the Semi-diameter of the Globe AB.

3. The Cone CDE will be equal to the Globe ABD.

XI. To make a Cube equal to a given Globe.

1. Make a Cone equal to a Globe, by the foregoing Problem.

2. Make a Parallelepiped equal to this Cone, by Prob. 5. of this Chapter.

3. Lastly, make a Cube equal to this Pa∣rallelepiped, by Prob. 6. of the same Cha∣pter.

Here we conclude our Treatise of Geome∣try, being perswaded, that the things which we have said, will be enough for those who would make any Progress in Fortification.