the sweep being 203 inches as before is said is alwayes one side throughout the whole Work of the same Rising line is 41209 as is found in the second page the third line the other fide from the point A to F is 9 foot or 108 inches whose square is 11664 found in the first page and the 28th line now substract the square made of the side A F 11664 from the square of the side D E so remaineth 29545 41209 11664 29545 Seek in the Table of squares for that number and I finde in the second page and 12 line and the sixth Columne 29584 the nearest number to it yet it is a little too much near the ¼ of an inch and toward the left hand in the same line the next Column under the title feet inch you finde 14 4 signifying that to be 14 foot 4 inches and in one Columne more to the left hand and the same line you see under the Title of inches 172 over the head you tituled inches which must be subracted from 203 inch so remaineth 3 inches for the Rising of F E which is 2 foot 7 inches as in the first page of the Table and the 31 line 203 172 031 These few Examples I think may be sufficient to shew the use of the following Tables of squares the benefit where of may be very great for such as shall make use of the same If any desire the finding of the Fractions of these squares when he findeth not his just figures in the squares let him do thus substract the Figures under his number from the Figures above his number which shall be the denominator then these Figures given substracted from which the next squares less shall be the denominator to that Fraction As for Example In the foregoing figures after substraction should have been 29553 the nearest agreeing in the Tables is 29584 the next lesser square number in the Table is 29241 which is more a great deale too little then the other is too great then substract the lesser square number 29241 from 29584 and so resteth 343 which must be the denominator then again substract the true number given 29553 the next lesser square number in the Table is 29241 which must be substracted I say from the true number given 29553 and so resteth after substraction 312 which is the Numerator to the Fraction and must be thus written â— so then the number belonging to 29584 is 171 inches and 312 343 parts of an inch which being abreviated is something more then ¼ of one inch and not full â…ž of one inch 29584 29241 343 Thus he that pleaseth may finde the rising of any Timber or narrowing of any place by these Tables and the help of Substraction exactly to any Circle whatsoever but it may suffice that a Man going to his Tables may see which square his figures have greatest affinity with and may estimate the difference near enough without seeking for the fraction which will be easily known by much practise herein HEre followeth a Table of Square Roots ready Extracted from one Inch to 1300 Inches which is to 108 foot and 4 Inches and it is thus contraved That from one Inch to 840 Inches all the Inches are reduced into Feet and Inches for the ease and help of Workmen who alway take their Measures by Feet and Inches but from thence to the end of the table you have the Inches onely and the Squares thereof against them as the Titles over every Page do make appear A Table of Square Roots Inch Feet Inches Squares 1  1 1 2  2 4 3  3 9 4  4 16 5  5 25 6  6 36 7  7 49 8  8 64 9  9 81 10  10 100 11  11 121 12 1 00 144 13 1 1 169 14 1 2 196 15 1 3 225 16 1 4 256 17 1 5 289 18 1 6 324 19 1 7 361 20 1 8 400 21 1 9 441 22 1 10 484 23 1 11 529 24 2 00 576 25 2 01 625 26 2 2 676 27 2 3 729 28 2 4 784 29 2 5 841 30 2 6 900 31 2 7 961 32 2 8 1024 33 2 9 1089 34 2 10 1156 35 2 11 1225 36 3 00 1296 37 3 1 1369 38 3 2 1444 39 3 3 1521 40 3 4 1600 41 3 5 16â—1 42 3 6 1764 43 3 7 1849 44 3 8 1936 45 3 9 2025 46 3 10 2116 47 3 11 2209 48 4 00 2304 49 4 1 2401 50 4 2 2500 51 4 3 2601 52 4 4 2704 53 4 5 2809 54 4 6 2916 55 4 7 3025 56 4 8 3136 57 4 9 3249 58 4 10 3364 59 4 11 3481 60 5 00 3600 61 5 1 3721 62 5 2 3844 63 5 3 3964 64 5 4 4096 65 5 5 4225 66 5 6 4356 67 5 7 4489 68 5 8 4624 69 5 9 4761 70 5 10 4900 71 5 11 5041 72 6 00 5184 73 6 1 5329 74 6 2 5476 75 6 3 5625 76 6 4 5776 77 6 5 5929 78 6 6 6084 79 6 7 6241 80 6 8 6400 81 6 9 6561 82 6 10 6724 83 6 11 6889 84 7 00 7056 85 7 1 7225 86 7 2 7396 87 7 3 7569 88 7 4 7744 89 7 5 7921 90 7 6 8â—00 91 7 7 8â—81 92 7 8 8464 93 7 9 8649 94 7 10 8836 95 7 11 9025 96 8 0 9226 97 8 1 9409 98 8 2 9604 99 8 3 9801 100 8 4 10000 101 8 5 10201 102 8 6 10404 103 8 7 10609 104 8 8 10816 105 8 9 11025 106 8 10 11236 107 8 11 11449 108 9 0 11664 109 9 1 11881 110 9 2 12100 111 9 3 12321 112 9 4 12544 113 9 5 12769 114 9 6 12996 115 9 7 13225 116 9 8 13456 117 9 9 13689 118 9 10 13924 219 9 11 14162 120 10 0 14400 121 10 1 14641 122 10 2 14884 123 10 3 15229 124 10 4 15376 125 10 5 15625 126 10 6 15876 127 10 7 16029 128 10 8 16384 129 10 9 16641 130 10 10 16900 131 10 11 17161 132 11 00 17424 133 11 1 17689 134 11 2 17956 135 11 3 18225 136 11 4 18496 137 11 5 18769 138 11 6 19044 139 11 7 19321 140 11 8 19600 141 11 9 19881 142 11 10 20164 143 11 11 20449 144 12 00 20736 145 12 01 21025 146 12 2 22416 147 12 3 21609 148 12 4 21904 149 12 5 22201 150 12 6 22500 151 12 7 22801 152 12 8 23104 153 12 9 23409 154 12 10 23716 155 12 11 24025 156 13 00 24336 157 13 1 24649 158 13 2 24964 159 13 3 25381 160 13 4 25600 161 13 5 25921 162 13 6 26244 163 13 7 26569 164 13 8 26956 165 13 9 27225 166 13 10 27556 167 13 11 27889 168 14 00 28224 169 14 1 28561 170 14 2 28900 171 14 3 29241 172 14 4 29584 173 14 5 29929 174 14 6 30276 175 14 7 30625 176
29 foot as you may see by dividing it by 12 or else if you turne to the Tables and seek under the Title of Inches for 348 you will see in the same line toward the left hand 29 feet which you will finde in the third Page and the 28th line the seventh and eighth Column then I Work by that Sweep to 3 5 of the length of the Rising line or 12 foot of the same at the point C it is represented at which point I seek the Rising C B I seek in the Table for the Square made of 144 and I finde it in the second Page 24 line at the first Columne and toward the right hand under the Title of Squares I finde 20736 which is the Square made of 144 then I seek for the Square made of the Sweep or side A B 348 inches and I finde it in the Tables to be 121104 from this 121104 I Substract the other Square made of the side D C 144 being 20736 and there remaineth 100368 whose Root I finde in the Tables in the third Page and the 37th line and the sixth Columne 100489 which is too much by neare 121 but the other number afore it being much more too little the number answering hereunto is 316 inches and near ¼ Substracted from 348 the whole side leaveth 31 inches ¼ or two foot 7 inches ¼ for the Rising 0 30 57600 600 9666 89 121104 20736 100368 at the point C Now to make a rounder Sweep aftward on or at the other end of the line as from B to F which runeth higher up or Roundeth more as from I to F Here will be something more of trouble to finde the Sweep that shall exactly touch the two points assigned as from B to F then to finde the former Sweep Now the Demonstration wil shew it to be thus Let B and F be the two points to which the Sweep is confined to touch draw a streight line from B to F as you see and so you have a Right lined Triangle made of the sides B H the length of the line to be swept by the second Sweep and the side H F the height of the same together with the Subtending side B F then a streight line drawn from the middle of the side B F and perpendicular or square to the same line B F and extended till it touch the side D A the place where it toucheth shall be the Centre of the same Sweep as is the line G H passing through the middle of the side B F at the point O which to finde Arithmetically proceed thus finde first the length of the side B F as before is taught of two sides of a Right Angled Triangle given to finde the third side which will be found to be 134 ½ inches the halfe whereof is 67 inches ¼ from B to O then if a perpendicular be let fall from O to the line B H it will cut that Base line also in halves as at the point P being 48 inches then again finde the side O H and that will be in this Example equall to the side B O but in other cases it may not so fall out So then those two sides being known as the side O H 67 ½ inches and the side P H 48 inches and the whole length of the side K H 240 inches you may then Work by the Rule of Three saying if 48 the side P H give 67 ½ inch for the side O H what will 240 give for the side K H as thus If 48 give 67 ½ what will 240 240 2 67 144 1680 4640 1440 16080 335  48888 16880 44 If you Multiply the two first numbers together and divide by the first number you will beget in the quotient 335 for the length of the whole side G H. I here neglected the ½ inch in this Multiplication for the ½ inch should have been Multiplied into the 240 by adding to the Summ 16080 120 the halfe of 240 and it maketh 16200 which divided by 48 maketh 337 ⅓ inches for the whole side G H So then these two sides being found find the side G K thus as before is taught look in the Table of Squares for the Square made of the side 337 and it will be 113569 from which Substract the Square made of 240 the other side being 57600 there resteth 55969 as you may see for that number sought for in the Tables and you find the nearest number to it to be 56069 and the roote of it to be 237 for the side G K to which must be added the Rising of the point C B or K D which is all one and is as we found it before to be 31 ¼ inches added to 237 maketh 268 ¼ inches or 22 foot 4 inches shewing that at 22 foot 4 inches from the point D towords G will be the point where the Centre of the Rounder Circle ought to stand Then again you have the side G K found as before to be 237 and the side K B 144 and if you work as is taught before but remember that if the longest side be sought for as is now in the last side sought for G B being the longest side you must add the squares made of the other two sides together and the square of those two Summs shall be the longest side G B 277 inches that is 23 feet 1 inch which is the length of the second Sweep and so have you the length of the Sweep The same order you may observe to round your Sweep as often as you please 113569 57600 55969 237 31 ¼ 268 ¼ If any have knowledge of the Doctrine of Triangles it may be found more readier that I leave to those that know the use thereof Note also that when you seek for any number in the Tables take heed that you minde the number of Figures you seek for to agree in number with those that directeth you to seek for them As for Example In the other figures abovementioned 55969 they are in number 5 by their places as you see then repairing to the Table I finde 559504 but telling the Figures I see that they are in number 6 but should be but 5 therefore this number represented in the seventh Page and the 28th line and third Columne is not the place I seek for then I turne toward the beginning of the Table till I see that the Columnes of Squares contain but 5 figures and there seek the nearest number agreeing to 55969 and in the second Page 37th line last Column I finde 56069 the nearest agreeing to it which is the place answering to the other directory figures Note also That the Example of finding the Sweep aforegoing is laid down by the small Scale of the Draught by which you may trie it for your better directions And in that Table you may see that any farther then 70 foot being the end of the seventh Page I have not mentioned the Feet and Inches belonging to the number of Inches but have left
Description and use of three general Quadrants accommodated for the ready finding the Hour and Azimuth universally in the equal Limbe The Compleat Modellist shewing how to raise the Model of any Ship or Vessel either in proportion or out of proportion and to find the length and bigoâ—ss of every Rope in all Vessels exactly with the weight of their Anchors and Cables There is a new Book called the Pilots Sea-Mirror which is a Compendium of the largest Wagoner or the lightning Sea-Collumbe Containing all Distances or thwart Courses of the Eastern Northern and Western Navigations with a general Tide Table for every day and the Change and Full of the Moon exactly for eight years also Courses and Distances throughout the Straights Printed for George Hurlock at Magnus Church Corner by London Bridge The Saints Anchor-hold in all stormes and Tempests Published for the support and comfort of Gods people in all times of Trial by John Davenport Pastor of the Church in New-Haven in New-Ingland There will shortly be made publick a Book Intituled The Mariners Compass Rectifled containing First a Table shewing the hour of the day the Sun being upon any point of the Compass Secondly Tables of the Suns rising and setting Thirdly Tables shewing the points of the Compass that the Sun and Stars rise and set with Fourthly Tables of Amplitudes all which Tables are Calculated from the Equinoctial to 60 degrees of Latitude with Tables of Latitudes and Longitudes after a new order with the description and use of all those Instruments that are in use in the Art of Navigation either for Operation or Observation THE COMPLEAT Ship-wright CHAP. 1. Of Geometricall Problemes BEfore we proceed to draw the Draught of any Ship or Vessel it will be necessary to be acquainted with some terms in Geometry as to know what a Point and a Line meaneth which every Book treating of Geometry plainly teacheth and therefore we shall passe that by supposing that none will endeavour to study the Art of a Ship-wright that is ignorant of these things and therefore leaving these Definitions I will proceed to some Geometrical Problemes necessary to this Art PROB. 1. How to draw a Parallel Line PArallel lines are such lines as are equidistant one from another in all parts and are thus drawn Draw a line of what length you please according to your occasion as the line A B then open the compasses to what distance you pleas or as your occasions require and set one foot of the compasses towards one end of the given line as at A with the other foot make a piece of an arch of a circle over or under the given line as the arch C keeping the compasses then at the same distance make such another arch towards the other end of the line setting one foot in B and with the other describe the arch D then laying a Ruler to the outside of these two arches so that it may exactly touch them draw the line C D which will be parallel to the given line A B or equidistant for so signifieth the word Parallel to be of equal distance PROBL. 2. How to erect a Perpendicular from a point in a right line given LEt there be a point given in the line A B as the point C whereon to raise a perpendicular Set one foot of the compasses in the given point C and open them to what distance you please as to the point E make a little mark at E and keeping the compasses at the same distance turn them about and make a mark at the point F in the line A B Then remove the compasses to one of those marks at E or F and seting one foot fast therein as at the point F open the other foot wider and therewith draw a small arch over the point C as the arch D then keeping the compasses at the same distance remove them to E and seting one foot in E with the other foot draw another little arch so as to crosse the former arch in the point D through the crossing of these two arches A D draw a line to the given point C as the line D C which shall be perpendicular to the line A B. Diverse other wayes there are to raise a perpendicular which I shall leave to the farther practice of such as desire diversity of wayes and proceed to the raising of a Perpendicular on the end of a line PROBL. 3. To raise a Perpendicular on the end of a line DRaw a line at pleasure or according to your worke as the line A B On the end thereof as at B set one foot of the Compasses and open them to what widenesse you please as to C and keeping fast one foot at B pitch one foot by adventure in C then keeping one foot of the compasses in C and at the same distance remove the foot that was in B to the point D in the line A B then keeping the compasses stil at the same distance lay a ruler to the points D and There are other wayes to effect this which I shall leave to farther practice of the learner this being the properest for our purpose PROB. 4. From a Point given to let fall a Perpendicular upon a Line given FRom the point C let it be required to let fall a perpendicular upon the line A B proceed thus Fix one foot of the compasses in the point C and open them to a greater distance then just to the line A B and make with the same extent the two marks E and F in the given line A B then divide the distance betweene the two points E and F into two equall parts in the point D then lay a Ruler to the given point C and to the point D and draw the line C D which will be perpendicular to the given line A B. CHAP. II. Of your SCALE BEing perfect in the raising and letting fall of perpendiculars and in the drawing of Parallel lines you may proceed to draught but first I will unfold unto you the use of a Diagonall Scale of Inches and Feet whose use is to represent a foot measure or a Rule so small that a Ship of 100 foot by the Keel may be demonstrated on a common sheet of paper really and truly to be so many foot long and so many foot broad of such a depth and of such a height between the Decks And therein the first thing to be considered is the length of the platform and of the Vessel you intend to demonstrate to the end you may make your Scale as large as you can because the larger the Scale is the larger will the draught be and so the measure of the demonstration will be the larger and more easie to unfold The Scale adjoyning consisteth as you see of 12 feet in all 11 thereof are marked with figures downwards beginning at 1 2 3 4 and so to 11 the first at the top is sub-divided into inches by diagonal lines as the distance between the first line of
Starne as is the Arch FS the length whereof is 8 Foot which doubled is 16 Foot for the whole length which is â…˜ of the breadth 20 Foot the length of the Sweepe that sweepeth it is the length of the Starnpost to the bottome of the Keele 14 Foot â…“ then the Crooked line from the end of the Transom or from the point S and toucheth the Keele at the point p this Arch Sp is the narrowing line Abaft at the breadth and the Crooked pricked line within the Keele marked with TR is a Rising line to order a hollow Moulde by the Timbers are placed at 2 Foot Timber and Roome as you may see by the Scale the line drawne from the Poope to the Foar-Castle marked by the letters VW is a line signifying the breadth of the Vessell at the top of the side from the top of the Poope to the Fore-Castle the top of the Poop is in breadth 10 Foot halfe the breadth at the beame the use of this line is in ordering of the Moulds to stedy the Head of the Top-Timber Mould to find his breadth aloft CHAP. VI. Shewing the Making and graduating or marking of the Bend of Molds REpaire to some House that hath some Roome or other broad enough to demonstrate the breadth of the Vessell and height enough for the top of the Poope in the length of the Roome or else if you cannot finde such a Roome convenient lay boards together or planks that may be large enough for your business as in the following Scheame you see First a long square made for the breadth of the Vessell as in the following Figure IABK then make the Moulds by their Sweepes and make Sirmarks to them for the laying of them together in their true places off first the Mould for the Floare being made you may make a Sirmarke by the line EF on the head of the Floare Mould and another on the foot of the Navill Timber Mould at the same place to signifie that those two marks put together they are in their true places and will compare so when any Timbers are Molded by them those Sirmarks must also be marked off on the Timbers and so in putting the Timbers up in the frame a regard being had to compare Sirmarks with Hirmarks each Timber will finde his own place and come to his own breadth and give the Vessell that forme assigned her by your Draught if it be wrought by it and so for all the other Moulds In making your Moulds that they may be smaller and smaller upwards and not all of a bigness you may measure the depth of the Side in the Mid Ships Circular as it goeth from the Keele to the top of the Side as here the Side as it Roundeth is 26 foot and in depth at the Rounheads or at the end of the Floare is one Foot as m m and at the other end at the head of the Timber is but halfe a Foot as at n n so then drawing two lines as the lines n m represents the diminishing of the Moulds in thickness upwards as those two lines representeth as if you would finde the thickness of the Timbers at the breadth take your 2 Foot Rule and measure the length from the end of the Floare at the point F to I at the breadth in the crooked body and it is 11 Foot 9 Inches signified at the Sirmarks there those two lines shew the thickness to be 9 Inches and so thick ought the Moulds to be at the breadth of the Vessell Now I have briefly touched the Demonstration of a Ship by Projection I shall now come to an Arithmeticall way farr surpassing any Demonstration for exactness CHAP. VII Arithmetically shewing how to frame the body of a Ship by Segments of Circles being a true way to examine the truth of a Bow LEt A B represent the length of a Rising line 12 foot long or 144 inches the height whereof let be B C 5 foot or 60 inches to finde the side D E or D A the radius of the circle A C whereto A D is the Semidiameter multiply the side A B 144 inches in it self and so cometh 20736 which sum divide 144 144 576 576 144 20736 by the side B C the height of the rising 60 inches and so cometh 345 and 3â—6 60 which is abreviated 3 unto this 345 â— â— must be added again the height of the Rising the side B e 60 which make 405 3 of an inch which is the whole Diameter of the Circle the half whereof is 202 1 â— inches and something more near â— 4 therefore we will avoide the fraction and account it 203 inches or 16 foot 11 inches which is the length of the Sweep or the side D E and so in all other Sweeps given whatsoever the Rule is generall and holds true in all things as to finde the Sweepe at once that will round any Beame or other piece of Timber that is to be Sweept remembring that if it be a Beame you are to finde the Sweepe you take but the half of his length 23 3 20736 345 6000 66 Example As if the Beame be 30 foot in length and to round one foot you must Work by 15 the halfe length of the Beame and turne 15 foot into inches by multiplying 15 by 12 so cometh 180 inches remember the length of the Rising line if it be to finde the Sweepe it must be multiplied by it selfe or the halfe length of the Timber must be Multiplied in it selfe as 180 by 180 so cometh 32400 which must be divided by 12 the rounding cometh in the quotient 2700 to which must be added the 12 again the rounding of the piece and so it is 2712 the whole Circle the halfe of this 2712 is 1356 for the length of the Sweep and so in all other matters where the Sweepe is required This I read in Mr. Gunters Book where he calls it the halfe Chord being given and the Versed fine to finde the Diameter and Semidiameter of the circle thereto belonging Example in the Draught foregoing Where the length of the Rising line is from the point E to the point i 32 foot and half the height thereof is the line D i 10 foot turne both Summs into inches as 32 foot multiplyed by 12 produceth adding the ½ foot 6 inches 390 inches length for the Rising line then turn the height of the Rising into inches as 10 foot multiplied by 12 produceth 120 inches from which 4 inches must be substracted because of the dead Rising is 4 inches so then the height is 116 inches Now multiply the length 390 inches by it self 390 maketh 152100. 390 390 000 3510 1170 152100 This Multiplication of the summ 152100 must be divided by 116 inches the height of the Rising and so cometh in the quotient of the devision 1311 inches unto this 1311 inches must be added the 116 inches the height of the Rising 116 1427 and it maketh 1427 which is the whole 112 3323 46344
739600 861 741321 862 743044 863 744769 864 746396 865 748225 866 749956 867 753689 868 753824 869 755161 870 756900 871 758641 872 760384 873 762129 874 763776 875 765625 876 767376 877 769129 878 770884 879 772641 880 774400 881 777161 882 777924 883 779589 884 781456 885 783225 886 784996 887 786769 888 788544 889 790321 890 792100 891 793081 892 795664 893 797449 894 799236 895 801025 896 802816 897 804609 898 805904 899 808201 900 810000 901 811801 902 813604 903 815400 904 817216 905 819025 906 820836 907 822649 908 824464 909 826281 910 828100 911 829921 912 831741 913 833569 914 835369 915 837225 916 839056 917 840789 918 842724 919 844561 920 846400 921 847241 922 850084 923 851929 924 853746 925 855625 926 857476 927 859329 928 861â—84 929 863041 930 864900 931 866761 932 868624 933 870489 934 872356 935 874225 936 876096 937 877869 938 879844 939 881721 940 883600 941 885481 942 886364 943 889249 944 881136 945 893025 946 894916 947 896809 948 898704 949 900601 950 902500 951 904401 952 906304 953 908209 954 910016 955 912025 956 913936 957 915849 958 917764 959 919681 960 921600 961 923521 962 926444 963 928369 964 929296 965 931225 966 933256 967 935089 968 937024 969 939961 970 940900 971 942741 972 944784 973 946729 974 948676 975 950625 976 952576 977 954529 978 956484 979 958441 980 960400 981 962361 982 964324 983 966â—89 984 968256 985 970225 986 972196 987 974169 988 976144 989 978121 990 980100 991 982081 992 984064 993 986049 994 988036 995 990025 996 992016 997 994009 998 996004 999 998001 1000 1000000 1001 1002001 1002 1004004 1003 1006009 1004 1008016 1005 1010025 1006 1012036 1007 1014049 1008 1016064 1009 1018081 1010 1020100 1011 1022121 1012 1024104 1013 1026196 1014 1028196 1015 1030225 1016 1032256 1017 1034289 1018 1036324 1019 1038361 1020 1040400 1021 1042441 1022 1044484 1023 1046529 1024 1048576 1025 1050625 1026 1052676 1027 1054729 1028 1056784 1029 1058841 1030 1060900 1031 1060961 1032 1065024 1033 1067089 1034 1069156 1035 1071225 1036 1073296 1037 1075369 1038 1077444 1039 1079521 1040 1081600 1041 1082681 1042 1085764 1043 1087â—49 1044 1089936 1045 1092025 1046 1094116 1047 1096209 1048 1098304 1049 1100401 1050 1102550 1051 1104601 1052 1106704 1053 1108809 1054 1110916 1055 1113025 1056 1115136 1057 1117249 1058 1119364 1059 1120489 1060 1123600 1061 1125721 1062 1127844 1063 1129969 1064 1132096 1065 1134225 1066 1136358 1067 1138489 1068 1140624 1069 1142761 1070 1144900 1071 1147041 1072 1149184 1073 1151329 1074 1153476 1075 1155625 1076 1157976 1077 1159929 1078 1162074 1079 1164241 1080 1166400 1081 1168561 1082 1170724 1083 1172889 1084 1175056 1085 1177225 1086 1179396 1087 1181569 1088 1183744 1089 1185921 1090 1188100 1091 1190281 1092 1192464 1093 1194649 1094 1196836 1095 1199025 1096 1201216 1097 1203409 1098 1205604 1099 1207801 1100 1210000 1101 1212201 1102 1214404 1103 1216609 1104 1218816 1105 1221025 1106 1223396 1107 1225449 1108 1227664 1109 1229881 1110 1232100 1111 1234321 1112 1236544 1113 1238769 1114 1240969 1115 1242625 1116 1245459 1117 1247689 1118 1249924 1119 1252161 1120 1254400 1121 1256â—41 1122 1258884 1123 1261029 1124 1263376 1125 1265625 1126 1267876 1127 1270029 1128 1272384 1129 1274641 1130 1276900 1131 1279161 1132 1281426 1133 1283689 1134 1285956 1135 1288225 1136 1287496 1137 1292769 1138 1294094 1139 1297321 1140 1299640 1141 1301881 1142 1304164 1143 1306449 1144 1308736 1145 1311025 1146 1313316 1147 1315509 1148 1317904 1149 1320201 1150 1322500 1151 1324801 1152 1327104 1153 1329409 1154 1331716 1155 1334025 1156 1336336 1157 1338649 1158 1340964 1159 1343381 1160 1345600 1161 1347921 1162 1350244 1163 1352569 1164 1354396 1165 1357225 1166 1358556 1167 1361689 1168 1364124 1169 1366921 1170 1368900 1171 1371240 1172 1373584 1173 1375929 1174 1378276 1175 1380625 1176 1382979 1177 1383329 1178 1387284 1179 1390041 1180 1392400 1181 1394761 1182 1397124 1183 1399489 1184 1401856 1185 1404225 1186 1406606 1187 1408904 1188 1411124 1189 1413711 1190 1416100 1191 1418481 1192 1420864 1193 1423249 1194 1425639 1195 1428025 1196 1430416 1197 1432809 1198 1435204 1199 1437601 1200 1440000 1201 1442401 1202 1444804 1203 1447209 1204 1449616 1205 1452025 1206 1454436 1207 1456849 1208 1459264 1209 1461681 1210 1464100 1211 1466521 1212 1468944 1213 1471369 1214 1473796 1215 1476225 1216 1478656 1217 1480989 1218 1483924 1219 1485961 1220 1488400 1221 1490841 1222 1493244 1223 1495729 1224 1498246 1225 1500125 1226 1503076 1227 1505529 1228 1507984 1229 1510441 1230 1512900 1231 1515361 1232 1517824 1233 1520289 1234 1522656 1235 1525225 1236 1527696 1237 1530169 1238 1334244 1239 1535121 1240 1537600 1241 15400â—1 1242 1542564 1243 1545049 1244 1547536 1245 1550025 1246 1552516 1247 1555009 1248 1557504 1249 1560001 1250 1562500 1251 1565001 1252 1567504 1253 1570009 1254 1572416 1255 1575025 1256 1577536 1257 1580049 1258 1582564 1259 1585081 1260 1587600 1261 1590121 1262 1592644 1263 1595169 1264 1597706 1265 1600225 1266 1602756 1267 1605289 1268 1607824 1269 1609361 1270 1612900 1271 1615441 1272 1617984 1273 1620529 1274 1622076 1275 1625625 1276 1628176 1277 1530729 1278 1633464 1279 1635841 1280 1638400 1281 1640961 1282 1643524 1283 1645989 1284 1645656 1285 1651225 1286 1653796 1287 1656369 1288 1658944 1289 1661521 1290 1664100 1291 1666681 1292 1669264 1293 1671849 1294 1674336 1295 1677025 1296 1679616 1297 1682209 1298 1683804 1299 1687401 1300 1690000 CHAP. XI Shewing how to Hang a Rising line by severall Sweeps to make it rounder aftward then at the beginning of the same IF any be desirous to have a Rising line rounder aftward then it is at the foar part of it they must proceed thus first Work by the Sweep that they would have first and then begin again and finde the other Sweep that they would have the roundest An Example of this will make it more plain as in the following Figure will appear Let D E represent the length of a Rising line E I the height thereof 8 foot on the after end thereof first I finde the Sweep that Sweepeth it by Multiplying of 20 foot the length which is 240 inches for if you look in the Tables under the Title of Feet-Inches for 20 feet you will see in the next Columne toward the left hand 240 over head is written Inches signifying that in 20 feet is 240 inches and just against it and in the same line toward the right hand under the Title of Squares you will see written 57600 signifying that the square of 240 is 57600 these numbers you will finde in the second Page of the Tables and the last line the seventh eighth and ninth Columns This squared number 57600 made by the Multiplication of D E 240 inches must be divided by the height of the Rising line assigned E I 8 foot or 96 inches so remaineth in the quotient 600 to which must be added the height of the Rising as is afore taught and they make 696 which is the Diameter of the whole Circle the half thereof is 348 inches which is