How by Arithmeticall skill you may mount any great peece of Ordinance by an inch rule vnto 10 de∣grees of the quadrant, if you want a qua∣drant or other instrument.
First you must measure the iust length of the Cannon or bore of the peece: reduce that measure into inches, and double the same: afterwards multiply the number of inches so doubled by 22, and deuide by 7, and note what Page 56 the quotient number is, which quotient deuided by 360 the degrees contained in the whole circumference of e∣uery circle, the last quotient number will shew you the number of inches, and parts of an inch, that will make a degree in the quadrant for that peece.
Example.
Admit there is a Saker or Fawcon, whose concaue or bore containeth iust 7 foote in length, and that you de∣sire to know what parts of an inch rule will mount her to one degree of the quadrant, you must reduce 7 foote in∣to inches, and you haue 84 inches, that 84 doubled is 168, the which multiplied by 22 ariseth 3696, the which deuided by 7, the quotient will be 528; that quotient number being deuided againe by 360, wil yeeld 1 7/15 (that is) one inch and ½, wanting 1/15 part of an inch. So I affirme that any peece of Ordinance whose chase or bore is but 7 foote long, being mounted by an inch rule one inch and 7/15 parts, that peece shall lye iust the height she wold haue done if you would haue mounted her one degree of the quadrant. The like order is to be obserued in mounting any other peece of Ordinance by an inch rule, of what length soeuer. And note that in mounting any other peece of Ordinance, to any degree of the qua∣drant, by a Geometricall quadrant, you must put the rule of the quadrant into the peece mouth, lifting the peece vp or downe with a leauer or hand-spike towards the breech, till the plummet cut iust vpon that degree of the quadrant you desire.
But to mount her by an inch, you must place the rule vpon the highest part of the mettall at the breech of the peece, coyning the peece vp or downe, till through the sight or slit in your rule (be lifted to that part or deuisiō in Page 57 your rule that answereth the degrees you desire) you espie the Carnoize or highest part of the mettall at the mouth of the peece, and the marke, all 3 in a streight line.
If you would mount the same peece to 2 degrees of the quadrant by an inch rule, you must multiply the mea∣sure in your rule last found, being 1 inch 7/15 parts by 2, in the order of fractions, and you shall haue 44/15, the which 44 being the numerator of the fraction deuided by 15 the denominator, the quotient being 2 inches 14/15 is your desire; so may you affirme that 3 inches by the rule wan∣ting 1/15 part of an inch, will make 2 degrees by the qua∣drant.
And note, that looke how much you would haue your peece mounted by an inch rule for to answer any num∣ber of degrees vnder 10, either multiply that number by the number of inches and parts of an inch, that makes a degree of the quadrāt, or else working as you did the first conclusion, multiplying the first product by the number of inches desired, and deuiding that product by the numbers afore mentioned, your last quotient will resolue you of your desire.
Example.
I demaund how much the peece afore mentioned should be eleuated by an inch rule, to answere to 8 de∣grees of the quadrant?
Resolution.
Reduce the length of the bore of the peece into inches, as afore is shewed, doubling that measure, and it makes 168, as you see in the 1 conclusiō: which 168 inches mul∣tiplied by 22, yeeldeth 3696 inches, the which product afterwards multiplied by 8, ariseth 29568, which summe deuided by 7, the quotient is 4224: the same deuided Page 58 by 360, yeelds in the quotient 11 inches 11/15 parts of an inch, so many inches and partes of an inch must the same peece be eleuated to with an inch rule, to answere to 8 degrees of the quadrant, as by triall you may find.
