Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

PROP. VII. By the Semicircle to lay down on the Ground, any of the former Fortifications.

Having drawn the Plot of your Fort on Im∣perial* 1.1 paper, or Vellom, and if it be a Regular Fort you need not describe it but two half Ba∣stions from the Center, for that will be sufficient. Having such a Plate whose length is set down on each respective line, and all proper Angles expressed, will not only be usefull for laying down the Work, but for finding the Solidity of the Ramparts, Parapets, and the other Earth Works See Fig 76.

If it be in such a Place, that from the Center* 1.2 of the Fort, all the Angles may be seen, place your Semicircle at Z, and lay off all the An∣gles of the Center, which here is 60°; then mark out the Diametrical lines, and making them their due length, as by your Plate they appear to be, set Piquets, on all the P, P'^s upright with the Plane, Then take up your Instrument and place a Piquet at Z. Then lock-spit out all the Polygons PP. Then mark out the Gorges CP, then set out the Flanks CF, either at Right* 1.3 Angles, or as otherwise required. Then lock∣spit out the Flanks CF, and the Faces AF, ha∣ving first set off the Capital PA, so is the Fort lined out for the Ground-line.

But if there be Houses and Obstacles in the* 1.4 way, that from the Center all may not be seen, then must you mark out any one side and mea∣sure it, and at each End set off the Angles of

the Polygon, (which here is 120°) and draw side after side, untill all be finished: Then fi∣nish the Bastions as before, and here great care must be had, or else you will run into infinite Errours.

☞ But you have liberty Experimentally to alter any of the former proportions, as you have occasion, and as will best serve the Place; as you see by the fortifying a streight lined Figure: Fig. 77. wherein Count* 1.5 Pagan's or in Manesson's way it may not be al∣lowed without some alterations.

Notes

• * 1.1

  Fig. 76.
• * 1.2

  Case 1.
• * 1.3

  Fig. 76.
• * 1.4

  Case 2.
• * 1.5

  Fig. 77.