A brief TREATISE for the measuring of Glass, Board, Timber, or Stone, square or round. Being performed only by simple Addition and Substraction, and that in whole Numbers, without any Multiplication, or Division at all. By John Speidell Mathematitian, in Queenes-street, where you may have of these Books at all times. LONDON, Printed by Thomas Harper. 164● This I have written in brief to help all such as can but only Add and Subtract in whole numbers, which if any cannot do, if they please to repair to my house in Queen-street, I will teach them so much Arithmetic in half an hour. And for all such as desire to be more then ordinarily instructed in the Mathematics; Let them repair unto me, and I shall (God willing) give them such satisfaction in all the rules of Arithmetic, both in whole Numbers and Fractions, with the extractions of roots, the rule of Cough or Algebra, with such extraordinary brief rules for exchange, interest, valuing of Lands, Leases, Rents, Annuities, and Purchases, and with a briefer way for casting up of Tower bills for gold or silver, then hath hitherto been taught by any. As also by a new invention of mine to teach women or children above 10 years of age, to cast up any ordinary question of the rule of 3. or practice, in whole numbers, and with Fractions in a few hours. There also may any be instructed in Geometry and Astronomy, by practice and demonstration, with the use of several instruments for surv●ying of Lands, and plotting the same sundry ways, and taking of heights and distances by several instruments, with the use of both the Globes, the projection of the Sphere in plain by scale and compass, and the doctrine of right lined and spherificall Triangles, with the application thereof in dialling, navigation and fortification, after a briefer way than is extant by any writer of these times, with the use of the Ephemerideses, and other secret inventions to be taught in private. There also may you have particular rules and scales for measuring of glass, board, wainscot, plastering, tyling, brickworke, stone, or timber, square or round, and for reducing one figure into another, and cutting of any part or parts thereof sundry ways, for valuing of rents, leases, annuities, and purchases, and for interest, with rebates, after any rate per centum, to be done only by scale and comp●sse, also gauging rods for all kind of Cask great or small, and presently taught at first sight, for the help of such as are not seen in Arthmetick at all. There also may you have of the best Mathematical paper, etc. To measure glass or board. THis is 2 several ways to be done: First, by having only the breadth of your glisse or board, and thereby to find how much in length sh●ll make a superficial or square foot, or having the length and breadth to find how much that whole pane of glass, or that whole board containeth. Example. Let a board or a pane of glass be broad 9 inches, and it is required to find how much in length shall make a square foot: subtract ●ver from, 33625. the number belonging to the breadth of your board or glass, and the remainder being looks, sheweth how much in length shall make a square foot. Example. The breadth being 9 inches, the number thereunto belonging is, 15563. which taken from, 33625. leaveth, 18062. which being looked out against it stands, 1. fo. and 4. inches, and so much in length shall make a square or superficial foot: And after the same manner, if a glass or board be 8. inches broad, there will be found 1. foot and 6. inches in length to make a foot: And if your glass or board be broad 13½ inches there shall be found 10¾ inches in length to make a foot. The second way. Suppose a pane of glass to be broad 16. inches, and long 2 foot and 6. inches, and it is required to find how many square foot therein is contained. Take the numbers belonging to both the length and breadth, and add them together, and from that addition subtract ever the ●●●ber belonging to 1. foot, and the remainder being look showeth h●w many squ●re foot that whole pa●●e containeth. Example. Against. 2 fo. 6, is. 20792 Against 1 4. is ●. 18062 t●g●●●er. 38854 Against. 1. fo. is. 16812 — ●●st. 22●42 to which answers 3. fo. 4. in. and so much is contained in that whole pane of glass required. Again, suppose a board to be long 18. foot, and broad 16. inches, and it is required to find how many square foot that whole board containeth. Against. 18. fo. is. 29365 Against. 16. inches. 18062 together. 47427 Against. 1. fo. is. 16812 rest. 30615 to which answers 24. foot to be therein contained. And after the same manner, if a board be broad 14. ¼. inches, and long 17. fo. 5. ●/●. inches, then shall be therein contained 20. fo. 8. ¾. inches. To measure Timber or Stone. This is also to be done 2. ways. First, having the breadth and depth of your Timber to find how much in length shall make a solid or cubical foot; or having the length, breadth, and depth, to find how many solid foot the whole piece of Timber containeth. Forasmuch as almost no Timber is so broad and deep above as below, therefore take both the breadth and thickness about the middle of the piece, and suppose you find it thereabouts to be 15. inches broad, and 11 deep, and it is required to find howmuch in length shall make a solid foot. Add the Numbers belonging to the breadth and depth together, and subtract that addition ever fion 50437, and the remainder looked showeth how much in length shall make a solid foot. Against. 15. inches is. 17782 Against. 11. stands. 16435 together. 34217 Which subtract from. 50437 so rest. 16220 to which answers 10 ½. inches, and so much in length shall make a solid foot required. And after the same manner, if a piece be broad 18. inches, and deep 16, there is found that 6. inches in length shall make a solid foot. And being broad 9 ¼. inches, and deep 7. ¼. by proceeding after the same manner there shall be found 24. inches in length to make a solid foot, and not 1/●. quarter more. The other way by having the length, breadth, and thickness to find how much the whole piece containeth. Let the breadth and depth about the middle be 16. ½ and 10. ●/●. inches, and the whole length 17. fo. 8 ¼. inches, and it is required to find how many solid feet that whole piece containeth. Add the Numbers belonging to the length, breadth, and depth together, and from that Addition subtract ever this Number 33625. and the remainder looked, showeth how many foot that whole piece containeth. The number belonging to 17. fo. 8. in. ¼. the length is. 29289 To the breadth 18195 To the depth 16335 together 63819 Subtract ever 33625 so rest 30194 to which answers 21. fo. 9 in. ½. to be therein contained. For Stone. Suppose a Stone to be long 5 fo. 7. in. ½. broad 2. fo. 1. ¼. in. and deep 1. fo. 3. in. ½. and it is required to find how many solid feet that stone containeth. To the length is 24314 To the breadth 20043 To the depth 17924 together 62281 Subtract 33625 so rest 28656 to which answers 15. fo. 3. in. 1/●. to be therein contained. And after the same manner the length being 4. fo. the breadth 18. inches, and the depth 16. there is found that whole stone to contain just 8. solid foot. To measure round Timber called girt measure. This is also to be done a ways, either by finding how much in length shall make a solid foot, or to find how many solid foot the whole tree containeth; Gird your tree about near the middle thereof, and suppose you find it to be 35. inches about, and you desire to find how much in length shall make a solid foot. Take the number belonging to the circomference, and double it ever, which double subtract from 61431. always the remainder being looked, showeth how much in length shall make a solid foot, which by so working is found to be 1. fo. 5. ¾. inches. And after the same manner, a tree being 2 fo. 7. inches about, there shall be found 1. fo. 10 ½. inches in length to make a solid foot. To find how much the whole Tree containeth. Suppose your tree near the middle to be about 48. inches, and long 14. fo. and it is required to find how many solid foot that whole tree containeth. Set down always twice the number belonging to the circumference, and under it the number belonging to the length, and under that ever this number 55381. then add all together, and cast away always the first figure thereof next your left hand, the rest looked showeth how many solid ●o. the whole tree containeth. Example. It is 4. fo. about, and the number thereunto belonging is. 27833 which I set down again. 22833 to 14 fo. ●he length belongs 28274 and ever this number. ●5381 fa. ●●●●● too which answers 17 fo. 9 ¾. inches, and so many solid foot that whole tree containeth, 〈◊〉 like manner work for all other. The use of a scale of Fractions, invented by John Speidell, Mathematitian, in Queen street. THE scale containeth 120. equal parts, being numbered on the left hand by 4. 8. 12. to 120. and on the right hand by 1. 2. 3. to 20. whose uses follow. Addition in Fractions. Let it be required to add ⅕. and ⅙. together: Take from the bottom the distance to ⅕. and setting one foot in ⅙. turn the other foot ever upwards, and it endeth now in 11/30. or you may take ⅙. first, and then setting one foot in ⅕. turn the other ever upwards, and it endeth also in 11/30. and so is found that ⅕. and ⅙. being added together do make 11/30. of the whole. In like manner ⅓. and ¼. of any thing being added together do make 7/12. of the same thing, be it of an ell, a yard, a shilling, or a pound, etc. Again, let it be required to add ⅔. and ¼. together; if now you take ⅔. from the bottom, and with that distance setting one foot in ¾. and turn the other foot upwards, as before taught, you shall find it to go beyond your scale. Therefore take only the distance between ⅔, or ¾. one of your Fractions given, and the top 120. and with that distance setting 1. foot in the other Fraction, turn downwards, and to what it showeth add ever 1. whole unite, as if you take the distance between ¼. and the top of your scale 120. and with the same distance setting one foot in ⅔. the other Fraction, turn downwards, and it endeth now in 5/12. to which add 1. whole unite, so is it 1 ●/12. and so is found that ●/●. and ¼. being added together do make 1 ●/1●. the thing required. And after the same manner 4/●. and ⅚. being added together do make 1 19/●0 and 7/●. and ●/● being added together do make 1 1●/24. parts, etc. Substraction in Fractions. Let it be required to take ⅖. from ½. and to find what part of the whole is left. Take only with your compasses the difference between ●/●. and ½. your 2. Fraction given, and that distance applied from the bottom, showeth 1/10. and so is found that 2/●. of any thing being taken from the 1/●. of the same thing, there shall remain 1/10;. of the same thing. And in like manner, if you take ⅙. from 3/●. there shall remain 13/10. and 2/●. being taken from ⅞. there shall remain ●/●4. and ●/5. from ⅚. leaveth 1●/●●. etc. Multiplication in Fractions. Multiplication and Fraction of Fractions, is one and the same thing; for it is all one question to say multiply ½. by ●/●. or what is the 1/●. of 3/●. or the 3/●. of 1/●? this is all one and the same demand, to do this by your scale of Fractions. Look out ⅗. on your scale, and against it on your left hand stands 72. whereof take ½. that is 36. which look also amongst the Numbers on your left hand, and by it stands ●/10. and so is found that ⅗. being multiplied by ●/●. or the 1/●. of ●/●. is ●/10. of the whole unite. And after the same manner, ●/●. of ●/4. is ½. of the whole, for against ●/●. stands 80. whereof ●/4. is 60. against which 60. stands 1/●. In like manner, if ⅘. be given to be multiplied by ●/●. the product will be found to be ●/1●. and 7/●. being given to be multiplied by ⅖. the product will be 7/20. etc. Division in Fractions. Let it be required to divide ●/5. by ½. Against 3/●. stands 72. and against 1/●. stands 60. now so often as 60 is in 72. which is once, and 1/●. so often is ●/●. in ●/●. etc. Again, divide 4/●. by ●/●. against ⅘. stands 96. and against ●/●. stands 40. now so often as 40. is in 96. which is two times, and ●/●. so often is ●/●. in ⅘. etc. Again, divide ●/●. by ⅚. against ●/●. stands 72. and against ⅚. stands 100 Now 100 cannot be had in 72. set it thus, 72/1●0. parts, or being abreviated by 4. it is 18/25. parts, and so is found that ●/5. being divided by ⅚. the Quotient is 18/25. etc. After the same manner 2/●. being given to be divided by ●/4. the Quotient will be ●0/●0. or abreviated by 10. it will be 8/9. etc. To find the value of a Fraction in shillings and pence. Let it be required to find how many shillings and pence the ⅝ of a pound is: Look out ⅝. on your scale, and among the Numbers on your right hand stands 12. below the ⅝. and 13. above it, that is to say the ⅝. of a pound is more than 12 shillings, and less than 13 shillings; now right against 12 shillings stands ⅗. count therefore in the small parts upwards, from ⅗. to ⅝. how many of them it is, and you find 3. which are two pences, so the 3. make ● pence, which put to the 12 shillings, so is it 12 shillings and 6 pence, and so is found that the ⅝. of 20 shillings, or a pound, is 12 shillings and 6 pence. Again, let be required to find how much the 2/●. of a pound is. Look ⅓. and the Number next under it on your right hand is 13. which stands against 13/20. then count the small parts form thence upwards to ⅓. which are 2. that is 2. two pences, which is 4 pence, so is found that ⅔. of a l. is 13. s. 4. d. and after the same manner ⅚. of a pound, is found to be 16. s. 8. d. and ⅞. to be 17. s. 6. d. etc. FINIS. 5 4 4 4 4 4 3 3 3 3 29827 30039 30241 30434 30618 30795 30966 31121 31267 31440 29832 30043 30245 30430 30622 30799 30969 31133 31290 31443 29386 30048 30249 30441 30626 30803 30973 31136 31294 31446 1 29841 30052 30253 30445 30630 30806 30976 31139 31297 31449 2984● 30056 30257 30449 30633 30810 30980 31143 3130● 31452 2985● 30060 30261 30453 30637 30813 30983 31146 31303 31455 29854 30065 30265 30457 30641 30817 30986 31149 3130● 31458 2 29859 30069 30269 30461 30645 30821 30990 31153 31310 31461 29863 30073 30273 30465 30648 30824 30993 31156 31313 31464 29868 30077 30276 30469 30652 30828 30997 31159 3131● 31467 2987● 30082 30282 30473 30656 30831 31000 31163 31319 31471 3 29877 30086 30286 30477 30660 30835 31004 31166 31323 31474 1 29881 30090 30290 30481 30663 30839 31007 31169 31326 31477 29886 30095 30294 30484 30667 30842 31011 31173 31329 31480 29890 30099 30298 30488 30671 30846 31014 31176 31331 31483 4 29894 30103 30302 30492 30674 30849 31017 31179 31335 31486 29899 30107 30306 3049● 30678 30853 31021 31183 31339 31489 29903 30111 30310 30500 30682 30856 31024 31186 31342 31492 29908 30116 30314 30504 30686 30860 31028 31189 31345 31495 5 29912 30120 30318 30508 30689 30864 31031 31193 31348 31498 29917 30124 30322 30512 30693 30867 31035 31196 31351 31501 29921 30128 30326 30515 30697 30871 31038 31199 31355 31504 29926 30133 30330 30519 30700 30874 31041 31202 31358 31508 6 29930 30137 30334 30523 30704 30878 31045 31206 31361 31511 2 29934 30141 30338 30527 30708 30881 31048 31209 31364 31514 29939 30145 30342 30531 30711 30885 31052 31212 31367 31517 29943 30149 30346 30535 30715 30888 31055 31216 31370 31520 7 29948 30154 30350 30538 30719 30892 31059 31219 31374 31523 29952 30158 30354 30542 30722 30896 31062 31222 31377 31520 29956 30162 30358 30546 30726 30899 31065 31225 31380 31529 29961 30166 30362 30550 30730 30903 31069 31229 31383 31532 8 29965 30170 30366 30554 30734 30906 31072 31232 31386 31535 29969 30175 30370 30558 30737 30910 31075 31235 31389 31538 29974 30179 30374 30561 30741 30913 31079 31239 31392 31541 29978 30183 30378 30565 30745 30917 31082 31242 31396 31544 9 29983 30187 30382 30569 30748 30920 31086 31245 31399 31547 3 29987 30191 30386 30573 30752 30924 31089 31248 31402 31550 29991 30195 30390 30577 30755 30927 31092 31252 31405 31553 29996 30199 30394 30580 30759 30931 31096 31255 31408 31556 10 30000 30204 30398 30584 30763 30934 31099 31258 31411 31559 30004 30208 30402 30588 30766 30938 31103 31261 31414 31562 30009 30212 30406 30592 30770 30941 31106 31265 31418 31565 30013 30216 30410 30596 30774 30945 31109 31268 31421 31569 11 30017 30220 30414 30599 30777 30948 31113 31271 31424 31572 30022 30224 30418 30603 30781 30952 31116 31274 31427 31575 30026 30228 30422 30607 30785 30955 31119 31278 31430 31578 30030 30233 30426 30611 30788 30959 31123 31281 31433 31581 30035 30237 30430 30615 30792 30962 31126 31284 31436 31584 21 22 23 24 25 26 27 28 29 30 3 3 3 3 3 3 3 2 2 2 31587 31729 31867 32000 32130 3225● 32378 32497 32613 32725 31590 31732 31870 32003 32133 32258 32380 32499 32615 32728 31593 31735 31872 32006 32135 32261 32383 32502 32617 32730 1 31596 31738 31875 32009 32138 32263 32385 32504 32620 3273● 31599 31741 31878 32011 32140 32266 32388 32507 32622 32735 31602 31744 31881 32014 32143 32269 32390 32509 32625 32737 31605 31746 31884 32017 32146 32271 32393 32512 32627 32739 2 31608 31749 31886 32019 32148 32274 32395 32514 32629 32742 31611 31752 31889 32022 32151 32276 32398 32516 32632 32744 31614 31755 31892 32025 32154 32279 32400 32519 32634 32746 31617 31758 31895 32028 32156 32281 32403 32521 32636 32749 3 31620 31761 31898 32030 32159 32284 32405 32524 32639 32751 1 31623 31764 31901 32033 32162 32287 32408 32526 32641 32753 31626 31767 31903 32036 32164 32289 32410 32529 32643 32755 31629 31770 31906 32038 32167 32292 32413 32531 32646 32758 4 31632 31772 31909 32041 32170 32294 32415 32533 32648 32760 31635 31775 31912 32044 32172 32297 32418 32536 32651 32762 31638 31778 31915 32047 32175 32299 32420 32538 32653 32765 31641 31781 31917 32049 32177 32302 32423 32541 32655 32767 5 31644 31784 31920 32052 32180 32304 32425 32543 32658 32769 31647 31787 31923 32055 32183 32307 32428 32545 32660 32772 31649 31790 31926 32057 32185 32310 32430 32548 32662 32774 31652 31793 31928 32060 32188 32312 32433 32550 32665 32776 6 31655 31796 31931 32063 32191 32315 32435 32553 32667 32778 2 31658 31798 31934 32066 32193 32317 32438 32555 32669 32781 31661 31801 31937 32068 32196 32320 32440 32558 32672 32783 31664 31804 31940 32071 32198 32322 32443 32560 32674 32785 7 31667 31807 31942 32074 32201 32325 32445 32562 32676 32788 31670 31810 31945 32076 32204 32327 32448 32565 32679 32790 31673 31813 31948 32079 32206 32330 32450 32567 32681 32792 31676 31816 31951 32082 32209 32333 32453 32570 32683 32794 8 31679 31818 31953 32084 32212 32335 32455 32572 32686 32797 31682 31821 31956 32087 32214 32338 32458 32574 32688 32799 31685 31824 31959 32090 32217 32340 32460 32577 32690 32801 31688 31827 31962 32092 32219 32343 32463 32579 32693 32804 9 31691 31830 31965 32095 32222 32345 32465 32582 32695 32806 3 31694 31833 31967 32098 32225 32348 32467 32584 32697 32808 31697 31836 31970 32101 32227 32350 32470 32586 32700 32810 31700 31838 31973 32103 32230 32353 32472 32589 32702 32813 10 31703 31841 31976 32106 32232 32355 32475 32591 32704 32815 31706 31844 31978 32109 32235 32358 32477 32594 32707 32817 31708 31847 31981 32111 32238 32360 32480 32596 32709 32819 31711 31850 31984 32114 32240 32363 32482 32598 32711 32822 11 31714 31853 31987 32117 32243 32365 32485 32601 32714 32824 31717 31855 31989 32119 32245 32368 32487 32603 32716 32826 31720 31858 31992 32122 32248 32370 32490 32605 32718 32828 31723 31861 31995 32125 32251 32373 32492 32608 32721 32831 31726 31864 31998 32127 32253 32375 32494 32610 32723 32833 ●● 32 33 34 35 36 37 38 39 40 By john Speidell in Queen-streete. 000●0 16902 19868 21614 22856 23820 24609 25276 25855 26365 03010 16990 19912 21644 22878 23838 24624 25289 25866 26375 04771 17076 19956 21673 22900 23856 24639 25302 25877 26385 06021 17160 20000 21703 22923 23874 24654 25315 25888 26395 1 06990 17243 20043 21732 22945 23892 24669 25328 25899 26405 07782 17324 20086 21761 22967 23909 24683 25340 25911 26415 08451 17404 20128 21790 22989 23927 24698 25353 25922 26425 09031 17482 20170 21818 23010 23945 24713 25366 25933 26435 2 09542 17559 20212 21847 23032 23962 24728 25378 25944 26444 10000 17634 20253 21875 23054 23979 24742 25391 25955 26454 10414 17709 20294 21903 23075 23997 24757 25403 25966 26464 1 10792 17782 20334 21931 23096 24014 24771 25416 25977 26474 3 11139 17853 20374 21959 23118 24031 2478● 25428 25988 26484 11461 17924 20414 21987 23139 24048 24800 25441 25999 26493 11761 17993 20453 22014 23160 24065 24814 25453 26010 26503 12041 18062 20492 22041 23181 24082 24829 25465 26021 26513 4 12304 18129 20531 22068 23201 24099 24843 25478 26031 26522 12553 18195 20569 22095 23222 24116 24857 25490 26042 26532 12788 18261 20607 22122 23243 24133 24871 25502 26053 26542 13010 18325 20645 22148 23263 24150 24886 25514 26064 26551 5 13222 18388 20682 22175 23284 24166 24900 25527 26075 26561 13424 18451 20719 22201 23304 24183 24914 25539 26085 26571 13617 18513 20755 22227 23324 24200 24928 25551 26096 26580 2 13802 18573 20792 22253 23345 24216 24942 25563 26107 26590 6 13979 18633 20828 22279 23365 24232 24955 25575 26117 26599 14150 18692 20864 22304 23385 24249 24969 25587 26128 26609 14314 18751 20899 22330 23404 24265 24983 25599 26138 26618 14472 18808 20934 22355 23424 24281 24997 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26928 27332 27701 28041 28357 28651 28927 2918● ●9430 29661 26937 27340 27709 28048 28363 28657 28932 29191 29435 29666 26946 27348 27716 28055 28370 28663 28938 2919● 2944● 29671 4 26955 27356 27723 28002 28376 28669 ●8943 2920● 29445 29675 26964 27364 27731 28069 28382 28675 28949 2920● 2945● 29680 26972 27372 27738 28075 28388 28681 289●4 2921● ●9455 29685 26981 27380 2774● 28082 28395 28686 28960 2921● ●94●● 29689 5 26990 27388 27752 28089 28401 28692 2896● 2922● 29465 29694 26998 27396 2776● 2809● 28407 28696 2897● 2922● ●9469 29699 27007 27404 27767 28102 28414 28704 2897● 2923● ●947● 29703 27016 27412 27774 28109 28420 28710 2898● 2923● ●9479 29708 6 27024 27419 27782 28116 28426 ●8716 28987 ●924● 29464 ●9713 2 27033 27427 27789 28122 28432 28722 28993 2924● ●9489 29717 27042 27435 27796 28129 28439 28727 2899● 2925● ●9494 29722 27050 27443 27803 28136 28445 28733 29004 29250 ●9499 29727 7 27059 27451 27810 28142 28451 28739 29●0● 29263 29504 2973● 27067 27459 27818 28149 28457 28745 29015 29269 29509 29736 27076 27466 27825 28156 28463 28751 29020 29274 ●9513 29741 27084 27474 27832 28162 2847● 28756 29025 29279 29518 29745 8 27093 27482 27839 28169 28476 28762 29031 29284 29523 29750 27101 27490 27846 28176 28482 28768 29036 29289 29520 29754 27110 27497 27853 28182 28488 28774 29042 29294 29533 29759 27118 27505 27860 28189 28494 28779 29047 29299 29538 29763 9 27126 27513 27868 28195 28500 28785 29053 29304 29542 29768 3 27135 27520 27875 28202 28506 28791 29058 29309 29547 29773 27143 27528 27882 28209 28513 28797 29063 29315 29552 29777 27152 27536 27889 28215 28519 28802 29069 29320 29557 29782 10 27160 2754● 27896 28222 28525 28808 29074 29325 29562 29786 27168 27551 27903 28228 28531 28814 29079 29330 29566 29791 27177 27559 27910 28235 28537 28820 29085 29335 29571 29795 27185 27566 27917 28241 28543 28825 29090 29340 29576 29800 11 27193 27574 27924 28248 28549 28831 29096 29345 29581 29805 27202 27582 27931 28254 28555 28837 29101 29350 29586 29809 27210 27589 27938 28261 28561 28842 29106 29355 29590 29814 27218 27597 27945 28267 28567 28848 29112 29360 29595 29818 27226 27604 27952 28274 28573 28854 29117 29365 29600 2982● 11 12 13 14 15 16 17 18 19 20