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end_n line_n perpendicular_a straight_a 1,765 5 14.0990 5 true
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A64318 The compleat gunner in three parts : part I. shewing the art of founding and casting ... the composition and matters of gunpowders ... : part II. discovers the necessary instruments ... to the compleating of a gunner ... : pt. III. shews the nature of fire-works / translated out of Casimir, Diego, Uffano, Hexan, and other authors; to which is added The doctrine of projects applyed to gunnery by those late famous authors Galilæus and Torricellio now rendred into English ; together with some excellent observations out of Mersennus and other famous authors. 1672 (1672) Wing T65; ESTC R29235 142,431 179

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your self just between your third Staff and your first mark there set up your fourth Staff then resort to your Angle again and standing behind the second Staff note whither a right line from the Angle to that notch before made on the subtendent Staff or side of the Triangle will direct you for that way precisely shall you go on until you come in a right line with the second and third Staff and erect there the fifth Staff this done measure the distance between the second and third Staff reserving that for a Divisor then multiply your distance between the first and third Staff by the distance between the fourth and fifth Staff the product divide by your reserved Divisor and it yieldeth in the Quotient the true distance between the two marks Example Let A B be the distance I would know C my first Station where the first Staff is erected I my Triangle made of three Staves and placed at the Station C directed with one of the containing sides to A which is the first mark as you may see in the Figure and with the other side to D and E the second and third Staves H is the notch or mark upon the side subtended to the Angle where the line visual from C passeth to the second mark B my Triangle now I scituate at D as it was before at C the one contained side lying even with the erected Staves the other directed to my fourth Staff F placed in a right line with E the third Staff and A the first mark Again my line visual proceeding from D to H the notch in the subrended side of the Angle is extended to my fifth Staff G scituated exactly between E the third Staff and B the other mark This done I measure the distance between my second and third Staff finding it 20 foot likewise between the fourth and fifth Staff and find it 72 foot finally between the first and third Staff 65 paces so that according to the Rule before given multiplying 65 by 72 I have 4680. which divided by 20 yieldeth in the Quotient 234 and so many paces is there between A and B. I have not set out the Figures in just proportions answering to these numbers for that is not requisite but in such form as may best open and make manifest the scituation of the Staves and Triangle wherein consists all the difficulty of this Practice CHAP. X. How you may readily find out the distance to any Tower Castle Forts c. by help of the former Quadrant LEt the Quadrant be made upon a square Board as is there marked A D B Q. Let D B be divided into 90 Degrees or equal parts and instead of the 12 equal parts or right and contrary shadows g m and h m let the two sides D Q and B Q be divided each into 1200 equal parts or as many as you please and marked from the Center A and have a Ruler or Index to be moved round upon the Center A● having two sights upon it set just upon the feducial line of the Index and let it be divided into such equal parts as the Lymb B Q or D Q. Let this Instrument thus fitted be handsomly placed upon its Staff or otherwise lay the feducial of your Index upon the beginning of the Degrees of the Quadrant and turn your whole Instrument the Index not moved till you may espy through the sight your mark then remove your Index to the contrary side of the Quadrant placing the line feducial on the side line where the degrees end and look through the sights and in that very line set up a mark a certain distance the farther the better this done take away your Instrument and set up a Staff there and remove the Instrument to the mark you espyed set your Index on the beginning of the Degrees moving your whole Instrument till you find through the Sights the Staff at the first Station then remove your Index your Quadrant keeping its place till you may again espy through the Sights your mark which done note the Degrees cut by the line feducial and then work thus upon some even smooth Superficies whether it be Board Plate or Paper Draw first a streight line and open your Compasses to some small distance call that space a score and make so many such divisions upon your Line as there is scores between your Stations then upon the end of your line raise a perpendicular and fixing one foot of your Compasses at the other end opening it to what wideness you please draw an Arch rising from the same line that represents your Stationary distance and dividing it into 90 equal parts or Degrees as you was taught in the making your Quadrant extend from the Center to the number of Degrees cut by your feducial line a right line until it concur with the perpendicular before erected then see how much of that space which representeth the score in dividing your Stationary distance is contained in the perpendicular so many score is the mark off from your first Station and by dividing the Hypothenusal line you may find the Distance from the second Station Example A the first Station C the second D the mark A C 80 paces Degrees of the Quadrant cut by the line feducial at the second Station is 71 d. ½ and H is the unity or measure representing one score E F 4 parts G F 12 G E 12 ⅔ or thereabouts Thus may you conclude the mark to be distant from the first Station 12 score paces the Hypothenusal line or distance of the mark from the second Station 12 score and 13 paces See the Figure To perform this Work by Calculation In the foregoing Figure B is the place to be measured A the mark where I first disposed my Instrument from it I go Orthogonally to C the Index suppose cuts there 400 in the right side of your square the distance between B and C I have supposed 80 paces wherefore multiply 1200 by 80 and there cometh 96000 wh●ch divided by 400 declareth unto me 240 paces the true length from A to B. Or by dividing 1440000 the square of 1200 with 400 the parts cut you shall produce in the Quotient 3600 your proportionable part found by the Rule of Reduction which augmented in 80 yieldeth 288000 and that divided by 1200 bringeth in the Quotient 240 which is the length A B agreeing with the former operation But if you would find C B or the Hypothenusal line being the distance between the second Station and the mark then by the former Table of Squares or with your Pen find the Square of A C and the Square A B the distance already found from the first Station these two Squares added together the Square Root of that Sum is the distance C B viz. 253 paces or if the Sum of the Square of A B and A C be sought for in the Table of Squares you will find against it 253 paces the length of C B which was