The third part of the principles of the art military practised in the warres of the United Provinces vnder the Lords the States Generall and His Highnesse the Prince of Orange : treating of severall peeces of ordnance ... : together with a list of all necessary preparations appertaining to an armie ... / written and composed by Henry Hexham.

THE MATHEMATICALL DESSOLVTION VPON THIS Antwerpian Question: Dedicated to all the Lovers of that noble Science, by Master John Stampion de John, Mathematician.

[illustration]

Sirs. The wing of fame hath of late fluttered out that now our ingenuity is brought to the tryall of the Touchstone, by proposing of a certain Question under the name of Senior John Bap∣tista of Antwerp, whose pate is swoln with selfe conceitednesse and pride, which being not worth the answering, I will come to the solution of it, ra ••her to give satisfact on to our Batavians, then to fulfill the desire of the Propounder: And this may serve as an introduction unto it, to the end, that the honour which he doth assume unto himself, may not wholy be appropriated to him.

THE DESSOLVTION.

LET this figure above of a Horn-work (as hee saith) be decyfered by H. whose breadth M. N. is known to be 34. Rodds, 7. foot, and 7. inches, and the required battered noted A. whose place is likewise found out by the known conditions. The first co ••dition is, that the violence of the Canon planted upon the battery A. beates with as much force upon the flanck E. D. as it doth upon the Face C. D. whence it is manifest, that the Angle of the espaule or shoulder EDC. being devided into two equall parts with the right line T. V. D. A. that then this battery of necessity must come to be in the right line T. D A. Secondly, that the face D. C. and I. G. and the distance D. G. may with the like Canon shot be flancked and beaten upon by the battery A. that is, when as the Angles I. A. G. G. A D. D. A. C. are alike one to the other, whence will follow, that through the five points, C. D. G. I and A. a circular circumference will passe. Now for that which concernes the third known part, namely, as that the batterie A. must be no further from C. then sixty rodd, or six hundred foot, A. being the greatest distance in the circumference as is in the third booke and fifteenth proposition which is taken from of the middle-line of Euclids propositions, we have found out accor∣ding

to this preparation, the middle line as C. Y. to be sixty rodds, the right line C. I. to be nine 34. rodds, 7. foot, and 7. inches, or 34. 77/00 and the lines I. G. G. D. and D. C. to be answerable one to another. Let G. now be the Center, Then substract I. G. and Q. D. cutting through C. I. in A. and F. then will I. A. or I. C. be alike to one of the lines, I. G. &c. because now Q. I. stands alike to I. G. as I. G. is alike to G. A. and by the fourth proposi∣tion of the sixt book, as Q. A. is alike to A. F. so also Q. G. is to G. D. or as I. G. is to G. A. the cube upon I. G. with the corps which is made upon the quadrate I. Q. as superfi∣cies, and the depth I. C. are together alike to the corps upon the Quadrate I. Q. as super∣ficies, and the depth to be three times the length of I. G. whence will follow, aswell by the corporall cutting of a dye, as we have shown in our New Algebra which shall shortly God willing come out in English, as by Sectione Com. by which I. G. is found to make 28. ½—V 263. ¼ so doth E. F. or D. C. likewise, and lastly the Angle E. D. C. being devided into two equall parts by the precedent T. D. then you have the cutting of A. in the circum∣ference out of Q. where your battery is to be cast up.

Now whereas Mr Stampion hath not expressed the finding out of the face G. I. by rea∣son of the little space contained therein, the more because he hath fully shown the Dissolu∣tion thereof in his new Algebra, we will here demonstrate the whole working thereof, how the face G. J. by his new Algebra annexed hereunto is to be found out.

The operation.

Setting down for G. I. x. so comes xxx + 31293 alike to 2700. x. or xxx—2700. x like to—31293. which is an equality in the third case of the Algebra of Mr. John Stampion, which being changed by the second case comes to be xxx—2700 x. as 3129. is alike, out of this vacant number 31293. is extracted a Cubice-root, 2700. times, the side as Mr. Stam∣pion teacheth in his new Algebra, pag. 112. and 113. comes the valuation of x 57. whereof the whole working shall here be set down as followeth.

The finding out of the first Letter.

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The finding out of the second letter.

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This 57. is now the valuation of x as xxx 2700. x is like to 31293. for the same value the signe—set down commeth 57, for the least valuation of the equality then in xxx—2700 x is alike to 31293. Now to find out by this 57. the length of the face, G. I. as followeth in the Rule fol. 138. of his new Algebra, that is, taking the half of 57. which is 28. ½ and multiply the same quadrate, and the product will be 812¼. whose tripple is 2436 ¾. and being substracted out of 2700. the number x. remaines 26; ¼ whose square root is V. 263. and being deducted from the half of 57. as being 28½ there remaines 28½.—V263. for the length of the face G. I. and E. F. and D. C. doth as much also.

Observe the manner of the Operation.

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