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. III. To fortifie a Hexagon according to Manesson Mallet's Proportion.

Now our Authour Monsieur Manesson Mallet, in his Works intituled Travaux de Mars, de∣viates from our former Authour, only in this: that as De la Mont did place his Flanks at Right Angles, he places them at 98 Degrees with the Curtains, and leaves no second Flank in all his Fortifications.

Therefore having described the Polygon PP,* 1.1 &c. divide PP into 1000 parts, prick off the Capitals PA 333, and the Gorges PC 200, then lay off the Flanks CF, 150 parts, at an Angle

of 98 deg. with the Curtain CC (by prop 5. §. 1. chap. 4.) and draw all the Faces, AF, AF, &c. Falling on C the point of the Flank and Curtain, so shall your Hexagon be fortified as was required.

III. Of the Dutch Fortifications.

The Emperour Ferdinand III. hath learnedly* 1.2 altered the Method of Fritach, Dogen, Gold∣man, and Faulhaberus, all which were Dutch Inginiers, and wrote large Volumes on this Subject; in his Works intituled Amussis Ferdi∣nandea, published 1654; by turning their way of working by Angles, into working by Sides.

Thus he setteth down a Catholick way of delineating the Sides, or Lines of any Fort by his 60 prop. thus, the Interior Polygon to be 66, the Capital 24, the Gorge 15, and the Flank 12. Or in making the Interior Polygon 22, the Capital 8, the Gorge 5, and the Flank 4. Or yet making the Interior Polygon 1000, the Ca∣pital 363, the Gorge 227, and the Flank 181, this is an Epitome of all the Dutch Fortifications, and is general excepting for the Square, which must have no second Flank.* 1.3

Notes

• * 1.1

  Fig. 74.
• * 1.2

  Fig. 74.
• * 1.3

  Fig. 74.