A BOOK NAMED TECTONICON briefly showing the exact measuring, and speedy reckoning all manner Land, squared Timber, Stone, Steaples, Pyllers, Globes. etc. Further, declaring the perfect making and large use of the Carpenter's Ruler, containing a Quadrant Geometrical: comprehending also the rare use of the Squire. And in th'end a little treatise adjoined, opening the composition and appliancie of an Instrument called the profitable Staff. With other things pleasant and necessary, most conducible for surveyors, Landemeaters, joiners, Carpenters, and Masons ⸫ Imprinted at London by Thomas Gemini, dwelling within the Black Friars: who is there ready exactly to make all the Instruments appertaining to this Book. ANNO. 1562. L. D. unto the Reader. Although (gentle Reader) many excellent in Geometry, upon infallible grounds have put forth diverse most certain and sufficient rules, touching the measuring of all manner Superficiecis: yet in that the art of numbering hath been required (yea, chiefly those rules hid, and as it were locked up in strange tongues) they do profit, or have furthered very little the most part: certes nothing at all, the Landemeater, Carpenter, or Mason, wanting the aforesaid: for their sakes I am here provoked not to hide, but to open, and so increase the talon which I have received: yea, to publish in this our tongue very shortly (if God give life) a volume containing the flowers of the Sciences Mathematical, largely applied to our outward practice, most profitably pleasant to all manner men of this realm. In the mean time I shall desire the Artificers above named to be contented with this little book (a taste of my good will towards them) which I wish even so to farther the readers, as I know it sufficient for the true measuring and ready account of all manner Land, Timber, Stone, Borde, Glass, Pavemeut. etc. Here mine advise shall be to those Artificers that will profit in this, or any of my books, now published, or that hereafter shall be, first confusely to read them thorough, then with more judgement, and at the third reading wittily to practise. So few things shallbe unknown. Note, oft diligent reading, joined with ingenious practice, causeth profitable labour. Thus most heartily farewell (loving Reader) to whom I wish myself present to further thy desire and practise in these. The pleasant profit, or content of this little book. And in what it exceedeth all other published. OTher Books tofore put forth in our english tongue contained only the bare measuring of Land, Timber, and Board: how agreeable in all places to the rules of Geometry, let the learned judge. Here (gentle Reader) thou shalt plainly perceive through diligent reading, how to measure truly and very speedily all manner Land, Timber, Stone, Steaples, Pillars, Globes, Board, Glass, Pavement. etc. without trouble, not pained with many rules, or obscure terms. Nor yet with the multitude of tables, as here before hath been: in which not a few errors were committed: for that cause no just account might any way be had. Further ye shall by this book understand the whole making and comely handling of the Carpenter's Ruler, with the true measures. etc. And his use appointed to the ready measuring of all kind of Timber, Stone, Borde. etc. Also the leveling of grounds, taking of heights, is pleasantly and diversely practised by the ruler. Ye have here not the common but the rare use of the Squire applied to heights, lengths. etc. and to the finding of the just hour of the day diverse ways: through the aid of pleasant tables, newly adjoined to my general Prognostication, by the which the proportion of things direct or squirewise standing, are by their shadows known. To conclude, in the end of this book is added a treatise showing the making and use of an Instrument, by which ye shall get lengths, heights, Breadths, widenesses, where, or how so ever they stand. Other necessary things are contained in this little volume, which I commit to the diligent Readers. diverse things conducible, to the art of measuring. THE I. CHAPTER. AS there are few craftsmen, which have all the kinds of Arithmetic readily: Characteres numeral. so I do suppose none so ignorant but that they do, or may easily perceive the simple significations of these Characters or figures. 1. 2. 3. 4. 5. 6. 7. 8. 9 0. and also their strength, in the first, second, and third rooms placed. Besides that, they must be familiar with these and such like Fractions. ½ ⅓ 1/7 1/16 1/32 ¾ ⅘ 9/10 The first leftwarde betokeneth one second part of an whole, Fractions. be it perch, inch, or any other measure: the next, one third, than one seventh part: the other ensuing, one sixteenth. So one thirty and two parts of an Inch. Then follow three fourths: four fifths. The last is nine tenths of an Inch: that is nine parts of an Inch, divided into ten portions. These I do intend to put in my ensamples, and in my tables, and margins following, to represent parts of perches or Inches. As, if I would write half an Inch after this manner. ½. Three quarters of an Inch, thus. ¾ One eight part of a perch, on this wise. ⅛. So of the rest. ¶ It is requisite also here to open what a perch, a Dayworke, a Rood, and an Acre is. Breadth. Acre. Length. So an Acre by statute ought to contain. 160 perches: the half Acre .80. perches: a Rood, commonly called a quarter .40. perches: a Day work .4. perches. Lo here the Acre expressed with his length and breadth. I must not omit here to tell you what thing is meetest to measure land with. Instruments to measuce with Poles cord knotted. They use commonly in the country, two peals, either of them the length of a perch. They are very good. Profitable staff. Yet for all kind of land, a cord .5. perches in length, well seared with wax & rosin, knotted or marked at the end of every perch, is more meet & readier. But in my fantasy, the Instrument Geometrical, which is put forth in th'end of this book, passeth all them & other, for the exact truth, & quickest speed. This instrument is so general & available to so sundry things, that it alone requireth a large book, if it should be sufficiently set forth. Now because practise and experience showeth me, that there is almost no land, but it may easily be brought by imagination, to a Triangle or Triangles, and so most truly measured: therefore to be short, this order shallbe taken. I will first figure and set afore your eyes Triangled Land, and other which by imagination shallbe brought into triangles. Then I shall teach the true measuring of them: I mean how to find a length & breadth, with which ye shall enter the Table of account following, where the acres, and odd perches, if there be any, shall appear. As these figures are measured, so all tryangled land, and other, brought into triangles, of what fashion soever they be, shallbe measured, And because it is requisite for true measuring of all triangles, to find a straight hanging line, I shall show first how that Line is to be found, imagined, or drawn. How the right hanging line in Triangles is drawn THE II. CHAPTER. To draw a hanging or plumb line. THis straight hanging line in all Triangles, is ever drawn or imagined from any Angle, cutting some one side of that triangle squirewyse: as ye may perceive the pricked lines in the triangles following. By the help of this line, all lands of Triangle fashion, are brought to be measured as ensueth. How to measure all manner Triangled Land. THE III. CHAPTER. IF thou be an Arithmetrician multiylie this straight hanging line, Euclid the first book, 41. pro. drawn as above as showed, in half the number of perches of that side which it cutteth squirewise. For want of that knowledge, take the aforenamed perches (I mean of the hanging line, and half the side which he cutteth) and with that Length and breadth enter your table of account, as there is set forth. So shall ye perceive the number of Acres, roods, dayworks. etc. Ensample. FOr the perfect measuring of triangles afore figured, and all other, suppose the second of these last. 9 figures on tother side, having written about it. a. b. c. d. to be a piece of land, whereof I would have the true measure. I find by a cord or otherwise, the pricked hanging line a. d. to be. 23. perches: the side b. c. which it cutteth squirewise. 44. perches, whose half is. 22. With these. 22. & 23. the convenient length and breadth, I enter the table of account. There I find by that table, at the corner where both the lines of conunient length and breadth do mete .3. Acres, 6. dayworks, and 2. Perches to be in that Triangle. Thus of all before figured. Here note, This Table followeth. your Table must ever be entered with all the perches of the hanging Line, and with half the side that he cutteth squirewyse: Or with the half hanging line, and the whole side cut. A figure of a double Triangle. THis figure e. f. g. h. is but two Triangles: and therefore measured as above in two parts: Or thus. The hanging line, e. g. is .33. perches: the side. f. h. that he cutteth squirewyse .20. perches, the half of the which is .10. Now enter your Table as afore, with 33. and .10. the convenient length and breadth. So shall ye find, 2, Acres, 2, dayworks and, 2, perches, the true content of this fygrue, e, f, g, h, a other ensample. None otherwise of the adjoined. n. o. p. q. and all other figures following, and other whatsoever they are, that by any means may be brought into triangles. Furthermore know, that the figure. i k. l. m. is readily thus measured. Add the perches of both the hanging lines together: so have ye. 23. With this number, and with half the perches of the side. i l. which he cutteth squyrewyse, being. 20. perches, enter your table: so is found as afore. These three figures following, although they may be measured by the rule of Triangles: yet for quicker speed, they have also their proper measuring as ensueth. How by supputation to measure all Triangled Land. To measure triangled land by supputation Join all the sides together: take half: out of that half pull every side, nothing difference. Then multiply the differences the one in the other: and the third difference augment in the product. That which increaseth multiply in the half of all the sides joined. Then the Radix of the surmontinge sum is the content of that Triangle. Four rules following. Now rest four rules to be treated of. The first for all manner regular square Superficies. The second for Round land, and her parts. The third for steeples, Columns, Globes, and their parts. The last for Mountains and Valleys. Here they shall in order follow. A rule for all manner regular or right squared land of many sides, as 5. 6. 7. 8. 9 10. 20. 100 etc. THE four CHAPTER. To measure land of many sides. MEasure and lay all the sides together, taking the half number of perches there contained. Then draw a right hanging line from the centre or mids of that figure, to the mids of some one side. And with that length and the other enter your Table. Note that the Triangle of all sides like, and the Quadrate figure, are also measured by this rule. Ensample. suppose this figure. a. b. c. d. to be a stresquare piece of land and every side .24. perches. The half sum of all sides is .72. perches: the right hanging pricked line, a. c. 21. perches. With these two numbers ye must enter your table of account following hereafter. And do as is opened in the declaration there adjoined, when numbers surmount the Table, as they do here. So shall ye find, 9 Acres .1. Rood, and. 8. dayworks, the content of this figure. a. b. c. d. Even thus is the other nynesquared figure measured, and all such like. A rule for round Land, and the parts thereof. The. V Chapter. Half the diameter multiplied in half the Circumference Archimedes in libello circuli mensurationis. showeth the content of any Circle. Or thus more plainly. Ye sshal enter your Table with half the number of Pearcches of the whole Circumference or compass, and with the number of half the diameter or breadth. So have ye the cotente. Ensample. suppose a piece of land, whereof the compass is 100 perches, the breadth 33. perches. I would know how much land is in this Figure. Enter your Table with half the compass that is .50. and with half the breadth that is .16. perches. Because in the table I can not find 50. for the greatest Length is .40. (therefore I enter with .40). and .16. So is found four Acres. Then I enter again with .16. perches remaining and .16. the breadth as before: that bringeth one Acre. Now to conclude, by addition of .1. and .4. I find .5. Acres in that round land, whose half compass is .50. perches. and the breadth .16. perches. FOr perfect knowledge and use of this Table following, when parts of perches are adjoined, note well this other example that ensueth, & also what is said of the declaration annexed unto the Table, How parts of perches are to be counted in measuring. when parts of perches are in the length, breadth, or in both. Imagine. f. g. h. to be a round piece of land: I find by measure the whole compass .99. perches. The half is .49. 2/1. The hanging Line or half breadth is .15. ¾. Enter your table with the whole perches, that is .49. and 15. leaving out. ½. and. ¾. which were but parts of perches. So have ye .4. acres .2. roads .3. dayworks, & .3. perches. For those parts of perches omitted at your first entering the table, work thus. The half perch, quarter, or other parts of a perch in the length, must be reckoned by themselves in the whole breadth: and those of the breadth contrariwise in the length. If there be such odd parts in both, then reckon them of the length in the whole breadth, and them of the breadth in the whole length: joining to the other aforegotten, remembering the product of the one fraction multiplied in tother, to be pulled from the increase. To make this matter plain, I will take this last ensample before. The one number wherewith I should have entered my Table, was .49. ½. the other .15. ¾. I found first by entering with .49. and .15. (omitting the odd parts) 4. acres .2. roods .3. Dayworks, and .3. perches. Now for the increase of the parts of perches left out: I must (as I said) reckon them of the length in the breadth, & contrariwise them of the breadth in the length. Half .15. ¾. is .7. perches & .7/8. Three quarters of .49. ½. is .37. perches. ⅛. Which added, makes .45. perches: This adjoined to the number aforegotten, bringeth the whole content of the round figure, which is .4. Acres .3. roods .4. dayworks .3. perches. & .5/1. of a perch, the product of the one fraction multiplied in tother subducted. What must be done when the numbers wherewith ye should enter exceed your table, counsel the declaration of your table there adjoined. Of the half Circle. To measure half circled land. FOr this half Circle, enter the table with half his compass, & with half the diameter of the circle, or with the length of the pricked hanging line, k. l. So the content of this half circle, is .2. acres .1. rood .7. dayworks .1. Perch, & .13/16. of a perch. another ensample of portions and parts of a Circle. suppose. n. m. o. following were a part of a Circle, or piece of land, whose content ye desired. The whole compass of the Circle which this portion representeth, is (as afore) .99. perches: his diameter or breadth .31. ½. The pricked ark or compass n. m. o. is .74. Now with the half breadth or semidiametre of the circle .15. ¾. & with .37. the half of the pricked compass: enter your table. So have ye .3. Acres .2. roods, 5. dayworks, 2. perches, and. ¾. of a perch, the content of the piece of Land full of Pricks, to the sides of the Triangle pricked. To measure parts of circled land. If ye desire to know the sum of perches in tother portion beneath the Triangle, separated by the line, m. o: ye must add the content of the triangle (which is .3. roods, and. ¾. of a perch, found by the rule of Triangles) to the Acres & perches before searched. So have ye .4. Acres .1. rood .5. dayworks 3. perches, and. ½. of a perch. This subtracted or pulled from the number contained in the whole Circle, the remain is the perches included in the small piece beneath the Triangle. That is .1. Rood .36. perches, and .1/8. of a perch. How mixed figures are measured. Land compound of circles or his parts. I Think none now will doubt how these two figures following are measured, because they are made of portions or parts of Circles, whose measure is before sufficiently opened: the one consisting of two half circles and a Quadrangle: the other being the portion of the Circle, m. o. doubled. If any evil fashioned land chance to be measure, which requireth to be brought in many triangles, to save labour, ye may add some portion unto that, and make it square or otherwise. So let it then be measured: and after from the product pull away that ye added: the remain is the content. To find the content superficial, of steeples, Columns, Globes, and their parts. TO the Arithmetician I say. For picked steeples, multiply the whole side in half the Circumference of the base, To measure steeples, Columns, Globes. etc. adding the plain of that base. For Pillars augment the Circumference of the base in the height, putting to the plain of both Bases. For Globes, the diameter in the Circumference multiplied: even so of fragments or Parts. Let them that be void of Arithmetic, enter my Table of account following, with such numbers as I now willed the Arithmetician to multiply, not forgetting what I have before written: So I serve their turn. Or thus, by the rule of proportion, the parts of a Globe are found. To measure parts of Globes. Suppose. a. b. c. to be a piece of a Globe, and .4. to be a Portion of the diameter, the whole being .14. Thus I say .14. The whole diameter giveth .616. the content superficial of this Circle: what shall .4. bring: So have ye .176. which is the content of that piece. To find the diameter by some known portion thereof. To find the unknown diameter of a Globe. IF ye be ignorant what length the diameter of that Globe is whose portion ye have: the height or part of the Dimetient being .4. foot, augment half the line. a. b, which is .6. ⅓. in himself, and the product divide by .4. So have ye .10. to be added to .4. which maketh .14. the whole diameter. The true measuring of Mountains and valleys. THE VI CHAPTER. To measure Mountains. FIrst ye shall measure the circuit of the foot, or base of the Mountain: then the compass of the summity or top: adding them together. So shall ye do of the Ascenses, that is, the going up from the foot to the top: joining the measure of the longer and shorter in one. Now take the half of the circuits added, and the half part of the Ascenses joined and enter your Table. There shall ye see the content. Ensample. A B. C. is the Mountain: a. c. the circuit of the base, being 100 perches: b. the top .16. perches. Which joined together make .116. F. c. the one ascense, Figure of a Mountain. is .55. perches: the other .75. These added make .130. The half of the circuits, is .58. the half of the Ascenses .65. With these two Sums ye shall enter your table of account: where ye shall find .23, acres 2. roads, and .10. perches, the true content of this figured hill. Of the Valley. To measure Valleys. AS in the Mountain ye measured the circuit or compass of the base or foot: so here contrary, ye shall meet round about the circuit, or compass of the height of the Valley. And as ye got the measure, or compass of the top of the Mountain: so measure the circuit of the depth of the eValley. In like manner as ye measured the ascense, that is, the going up from the foot to the top: so measure the descense, or going down of the Hill to the depth of the Valley. The rest all work, as I have showed in measuring the mountain. Figure of a Valley. For more plainness, behold this ensample, or figure. If ye lay together the circuits of the height and depth, which is .210 and .30. taking the half part of those two circuits, making an .120. than the two ascenses .140. &. 60, added in one produce .200. the half thereof being .100, with this, and .120. the other half of the circuit, ye may enter your table. That doing, lo .75. Acres. How this table of account now following is to be used WHen you have gotten a convenient Length & Breadth, (as I have above declared, by divers triangles & other figures) than you shall enter this table. Seek there the length and most number of Perches in the higher margin, which beginneth at .1. and endeth rightwarde at 40. Look tother sum of Perches (I mean the Breadth) in the right side, & hanging margin, from .1. descending to .30. Now at the meeting of the lines, where the one answereth the other directly in a square, you shall find the Acres, roods, dayworks & perches. Note that the first number set on the left side & upper part in any square, signifieth the number of Acres. The figure .1. set in the upper part & right side, doth betoken a Road: the figure .2. there two Rhodes .3. three Rhodes. Any figure in the left side beneath, signifieth a Dayeworke, or dayworks. A figure in the lower part ryghtewarde, declareth Perches. A declaration adjoined. what is to be done when numbers (with which you should enter) exceed your Table. WHen it chanceth that the one number or both with the which ye should enter this table, are greater than any here found: it behoveth you to take the half of th'one and the hole of the other, or what parts ye list of both most commodious for your purpose, and so enter your table. Look then what is there found, and it shall bear his name of the parts multiplied in themselves. Ensample. Suppose the number with the which ye should enter your table to be .103. perches in Length, and the Breadth .60. neither of these may be found in the margynes: wherefore I take the third part of an .103. which is .34. perches and .1. remaineth. The half of .60. that is .30. I find with entering them at the common meeting .6. Acres .1. Rode, & .5. dayworks. Look what I have showed in the .5. chapter of parts, that understand here of hole perches lest: subtracting. etc. This sum must have his name of the parts augmented in themselves. I took the third part of the one, and half the other number, therefore .2, must be multiplied in .3. or contrary, so have ye, 6. which signifieth that ye have found by entering, but the sixth part of that number ye should find Wherefore I must make this sum tofore found (being .6. Acres .1. Rode, and .5. dayworks) sixetimes as much. So have ye .38. acres & 1. Rode. For the perch remaining in the Length, reckon him in the breadth, (as is afore declared) in the .5. cha. of the remains: so have ye .60. Perches more to be added. So the increase of these two numbers .103. and .60. amounteth to .38. Acres, 2. Rhodes, & .5. dayworks. Thus any manner Length and breadth, is reduced to this Table following, which sufficeth. TABULA COMPUTATIONIS The Table of account. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1 1 4 1 2 1 1 1 1 2 1 3 2 2 1 2 2 2 3 3 3 1 3 2 3 3 4 4 1 4 2 4 3 5 5 1 5 2 5 3 6 6 4 6 2 6 3 7 7 1 7 2 7 3 8 8 1 8 2 8 3 9 9 1 9 2 9 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 2 2 2 2 3 3 2 4 4 2 5 5 2 6 6 2 7 7 2 8 8 2 9 9 2 2 1 1 2 2 2 2 3 3 2 4 4 2 5 5 2 6 6 2 7 7 2 8 8 2 9 9 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 2 1 3 3 3 4 2 5 1 6 6 3 7 2 8 1 9 9 3 2 1 1 2 2 3 3 2 4 1 5 5 3 6 2 7 1 8 8 3 9 2 1 1 1 3 2 2 3 1 4 4 3 5 2 6 7 7 3 8 2 9 1 4 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 1 4 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 5 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 5 6 1 7 2 8 3 1 1 2 2 3 3 5 6 1 7 2 8 3 1 2 2 2 3 3 5 6 1 7 2 8 3 1 1 2 2 3 3 5 6 1 7 2 8 3 1 1 2 2 3 3 5 6 1 7 2 8 3 6 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 6 9 2 2 3 2 5 6 2 8 9 2 1 2 2 4 5 2 7 8 2 1 2 3 4 2 6 7 2 9 2 2 3 2 5 6 2 8 9 2 1 2 2 4 5 2 7 8 2 7 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2 1 3 7 2 1 4 5 3 7 2 9 1 1 2 3 4 2 6 1 8 9 3 1 2 3 1 5 6 3 8 2 1 2 3 3 5 2 7 1 9 3 2 2 4 1 6 7 3 9 2 1 1 3 4 3 6 2 8 1 8 1 1 2 2 2 2 2 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2 1 3 1 3 1 3 1 3 1 3 2 8 6 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 9 2 2 2 2 2 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2 1 3 1 3 1 3 1 3 2 2 2 2 2 1 9 1 2 2 4 3 7 9 1 1 2 3 3 6 8 1 2 2 3 5 7 1 9 2 1 3 4 6 1 8 2 3 3 5 1 7 2 9 3 2 4 1 6 2 8 3 1 3 1 5 2 7 3 10 2 2 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 3 1 3 1 3 1 3 2 2 2 2 2 1 2 1 2 1 2 1 2 2 10 5 7 2 2 2 5 7 2 2 2 5 7 2 2 2 5 7 2 2 2 5 7 2 2 2 5 7 2 2 2 5 7 2 2 2 5 7 2 11 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 3 1 3 1 3 1 3 2 2 2 2 1 2 1 2 1 2 1 2 2 2 2 2 2 2 3 11 1 3 5 3 8 2 1 1 4 6 3 9 2 2 1 5 7 3 2 3 1 6 8 3 1 2 4 1 7 9 3 2 2 5 1 8 3 3 2 6 1 9 1 3 4 2 7 1 12 3 3 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 3 1 3 1 3 2 2 2 2 1 2 1 2 1 2 1 2 2 2 2 2 2 2 3 2 3 2 3 3 12 6 9 2 5 8 1 4 7 3 6 9 2 5 8 1 4 7 3 6 9 2 5 8 1 4 7 13 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 3 1 3 1 3 2 2 2 2 1 2 1 2 1 2 2 2 2 2 2 2 3 2 3 2 3 3 3 3 3 1 13 2 1 5 2 8 3 2 5 1 8 2 1 3 5 8 1 1 2 4 3 8 1 1 4 2 7 3 1 4 1 7 2 3 4 7 1 2 3 3 7 1 3 2 6 3 14 1 1 1 1 1 1 1 1 2 1 2 1 3 1 3 1 3 2 2 2 2 1 2 1 2 1 2 2 2 2 2 2 2 3 2 3 2 3 3 3 3 3 1 3 1 3 2 14 9 2 2 6 9 2 3 6 2 3 2 7 2 4 7 2 1 4 2 8 1 2 5 8 2 2 5 2 9 2 2 6 9 2 3 6 2 15 1 1 1 2 1 2 1 2 1 3 1 3 1 3 2 2 2 1 2 1 2 1 2 2 2 2 2 2 2 3 2 3 3 3 3 3 1 3 1 3 1 3 2 3 2 3 3 15 6 1 3 2 7 2 1 1 5 8 3 2 2 6 1 3 3 7 2 1 1 5 8 3 2 2 6 1 3 3 7 2 1 1 5 8 3 2 2 6 1 16 1 2 1 2 1 3 1 3 2 2 2 2 1 2 1 2 2 2 2 2 2 2 3 2 3 3 3 3 3 1 3 1 3 2 3 2 3 2 3 3 3 3 4 ●● 4 8 2 6 4 8 2 6 4 8 2 6 4 8 2 6 4 8 2 6 17 1 3 1 3 2 2 2 2 1 2 1 2 2 2 2 2 3 2 3 2 3 3 3 3 1 3 1 3 2 3 2 3 2 3 3 3 3 4 4 4 1 ●● 2 4 6 2 3 5 9 1 3 2 7 3 2 6 1 2 4 3 9 3 1 7 2 1 3 6 1 4 2 8 3 3 7 1 1 2 5 3 18 2 2 2 2 1 2 1 2 2 2 2 2 3 2 3 3 3 3 1 3 1 3 1 3 2 3 2 3 3 3 3 4 4 4 1 4 1 4 2 18 1 5 2 4 2 9 3 2 8 2 2 7 1 2 6 2 5 9 2 4 8 2 3 7 2 2 6 2 1 5 2 19 2 1 2 2 1 2 2 2 2 2 3 2 3 3 3 3 1 3 1 3 2 3 2 3 3 3 3 4 4 4 1 4 1 4 2 4 2 4 3 19 1 5 9 3 4 2 9 1 4 8 3 3 2 8 1 3 7 3 2 2 7 1 2 6 3 1 2 6 1 1 5 3 2 5 1 20 2 2 2 2 3 2 3 3 3 3 1 3 1 3 2 3 2 3 3 3 3 4 4 4 1 4 1 4 2 4 2 4 3 4 3 5 20 5 5 5 5 5 5 5 5 5 5 21 2 3 2 3 3 3 3 1 3 1 3 2 3 2 3 3 3 3 4 4 4 1 4 1 4 2 4 2 4 3 4 3 5 5 1 2● 1 5 2 3 6 1 1 6 2 1 3 7 2 1 7 2 2 3 8 3 1 8 2 3 3 9 4 1 9 2 4 3 22 3 3 3 1 3 1 3 2 3 2 3 3 3 3 4 4 1 4 1 4 2 4 2 4 3 4 3 5 5 5 1 5 2 2● 1 6 2 2 7 2 3 8 2 4 9 2 5 2 6 1 2 7 2 2 8 3 2 9 4 2 23 3 1 3 1 3 2 3 2 3 3 4 4 4 1 4 1 4 2 4 2 4 3 5 5 5 1 5 1 5 2 5 3 2● 2 1 8 3 3 9 2 5 1 1 6 3 2 2 8 1 4 9 3 5 2 1 1 7 2 3 8 2 4 1 24 3 2 3 3 3 3 4 4 4 1 4 2 4 2 4 3 4 3 5 5 1 5 1 5 2 5 2 5 3 6 2● 4 6 2 8 4 6 2 8 4 6 2 8 4 25 3 3 4 4 4 1 4 2 4 2 4 3 5 5 5 1 5 1 5 2 5 3 5 3 6 6 4 2● 6 1 2 2 8 3 5 1 1 7 2 3 3 6 1 2 2 8 3 5 1 1 7 2 3 3 26 4 4 1 4 2 4 2 4 3 5 5 5 1 5 2 5 2 5 3 6 6 6 1 6 2 2● 9 5 2 2 8 2 5 1 2 8 4 2 1 7 2 4 2 7 3 2 27 4 2 4 2 4 3 5 5 5 1 5 2 5 2 5 3 6 6 6 1 6 2 6 3 2● 2 1 9 5 3 2 2 9 1 6 2 3 9 2 6 1 3 9 3 6 2 3 1 28 4 3 5 5 1 5 1 5 2 5 3 5 3 6 6 1 6 1 6 2 6 3 7 2● 6 3 7 4 1 8 5 2 9 6 3 29 5 1 5 1 5 2 5 3 5 3 6 6 1 6 2 6 2 6 3 7 7 1 2● 1 7 2 4 3 2 9 1 6 2 3 3 1 8 1 5 2 2 3 30 5 2 5 3 6 6 6 1 6 2 6 3 6 3 7 7 1 7 2 3● 5 2 2 7 2 5 2 2 7 2 5 2 2 THus with few words is ended the certain measuring of all manner Land, touching their superficial contents. Wherefore now shall follow the true measuring of timber, Stone, Steples, pillars, Globes, according to their Crassitude. To the Reader. IT cometh commonly to pass that Carpenters, Masons, and such like Artificers are put either to measure Timber every way square, or squared logs, broader on th'one, thin on tother side, yea many times mutilate or unperfect stuff: some times. 3. 5. 10. or, 20, square in the head and so through, oftentimes round stone or timber, with hollowed. etc. Afore I show unto them what must be done with such pieces of Timber or stone to get their true measure, my desire shall be, that such craftsmen will leave to be heady or self-willed, yea so greedily to stick to their old corrupted rules that utterly they refuse to be taught. Both learning & experience declareth unto me, that the grounds which the best of them have are false. To open how and where, it needeth not: neither doth it appertain to instruction. Only it may suffice him that liketh the true way, here to receive it appointed to him. Yet to satisfy and content him which will not believe any such errors or false grounds to be: I say (and truly) that the Ruler of timber measure, which the more part of them hath, is not made by right art. Besides that their craft in seeking the square of some timber, is very false. They use in measuring to lay the broader and narrower sides together in a sum: and to take the half of that number for the square. Then they seek this untrue square upon the false ruler: and so measuring the timber, they conclude of it untruly. As this is corrupted, so are other grounds which they take to be infallible. Now to the purpose, touching the correction of those errors with other not mentioned, whereby true measuring may ensue this way shall be taken. After I have opened how ye must handle all such fashioned timber (as afore is spoken of) there shall follow a table, in which ye may find (as I will declare) the square of any stone, or timber. That known, it is requisite to have an other table immediately following, which may appoint to all true squares, from. 1. to. 6. inches, the just length to make a Foot every way square. In a foot square is contained 1728. Inches. With that length agreeable to your square, your log must be measured. And as oft as ye find it from the one end to tother of your timber, so oft ye may conclude the foot square to be contained in that timber log, or stone: that is, so many square seat there to be included. This Table of timber measure standeth in the place of a good Ruler, well docked with true measures. By this ye may make or correct rulers at pleasure, as after appeareth. Now orderly followeth the true measuring of all fashioned Timber or Stone afore named. How timber or stone, four square every way, or broader on the one then on the other side, is measured. THE VII. CHAPTER. IF a piece of Timber, or Stone be either equally square, or broader on the one side then on the other, ye shall take the just measure, I mean how many Inches the broader side containeth: even so of the narrower. This done ye must seek in the table of squares following, the measure of the broader side of the timber or stone, in the upper margin of that table. Then look for the number of Inches of the equal or narrower side, in the right part & hanging margine. At the common meeting, where the one number answereth directly to the other, there your true square shall appear. This square so found shall be referred to your table of timber measure: in the which ye may plainly see (if you run down by the left margin, until your Inches square appear) how many feet or Inches of your ruler belongeth to a foot square. As often as that measure there found is contained in the timber or stone, so often and as many feet square ye may conclude (without doubt) that piece of timber or stone to have. Ensample. suppose this squared Timber or Stone, a. b. c. d. were to be measured, the broader side, a. b, 20. Inches: the narrower side. b. c. 13. inches: the length. 40. inches. Now I must seek the broader side. 20. in the upper margin of the table. The narrower side. 13. must be found in the right side and hanging margin. At their common meeting: 16: inches, and. ⅛. part of an Inch shall appear. This true square must be searched for in the Table of timber measure. Therefore look for. 16. in the margin of that Table. In the squares with him rightwarde, ye shall sinned. 6. Inches, and. ¾. which is three quarters of an inch. Somedele less of your ruler then .6 and. ¼. laid out upon the Timber, maketh a foot square. And that measure so discreetly handled, is contained in the length of your timber sixetymes. Wherefore affirm six foot there to be, beside that is left .1/54. part of a foot. Note because the squares, at all times (as in this ensample) rise not to even Inches, but sometime to odd parts: Therefore according to your discretion, add or take away some part more or less in setting forth the foot square, as above is performed. It were intolerable tediousness, yea impossible, to set forth the true quantities of timber measure, to allodde quantities of squares. The discrete handling of these, the witty shall bring to a sufficient exactness. Of Timber or Stone. 3. 5. 10. 20. or mosides square. etc. THE VIII. CHAPTER. WHen Timber hath diverse equal squares in the head and so through: first measure all the square sides round about the head or end of the Timber. Then take half the number of the whole measure for th'one Breadth. Then measure from the Centre (which is the middle of the head, or end of the Timber) to the mids of one square side, between the two angles: and take the measure of that distance for the other Breadth. Now resort with the measures of these two breadthes (as tofore) to the Table of squares: seeking the bigger number or breadth in the upper margin, and the other less in the side margin. With the square there found, have recourse to the table of timber measure: and do as I have instructed. Ensample. ADmit this small piece of timber .5. square. e. f.. g. h. should be measured, every side being .12. Inches. If ye add together in one sum all the .5. sides, they make .60. Inches. The half is. 30. that serveth for one Breadth. Then the line. e. f. which goeth from the Centre or mids of the square to the middle of one side, is .8. Inches. The two numbers .30. and .8. must be sought (as afore) in the table of squares following. At the common meeting, your square shall appear .15. Inches and. ½. This square .15. seek in the table of timber measure. There ye may see right with it .7. Inches, and. ⅔. Now because of. ½. the odd quantity of the square above .15. Inches, lay sometime less. Then see how oftentimes that measure (so with discretion handled) is from the one end of your timber to the other: and affirm so many times a foot square there to be, as that measure is found in the length of your log. How round and hollowed Timber, steeples, Pillars, Globes. etc. are to be measured. THE IX. CHAPTER. FIrst gird the log round about with some line: then divide the line, which compassed that timber, in two equal parts, keep the one part for the bigger breadth: After ye shall divide again that whole length (the twenty and two part cast away) in three parts, and take the half of one of them for the other narrower Breadth. With the measures of these two breadthes, haste to your table, performing all thing as afore is opened. Ensample. suppose this little piece of Timber i k. l. m. were to be measured, the compass or gyrdinge 36. inches, the half of that is, 18. being the one breadth: then the third part of .36. is .12. the half of it is .6. which is the other narrower breadth. With these two numbers .6. and .18. enter the Table of squares following, and so the Table of Timber measure. At the last (all things performed as before) ye shall find in this round log, (the length. l. m. being. 18. inches). 1. foot and. ⅛. part of a foot. This is sufficient for all such like. A note of hollowed Timber. IF it chance that hollowed Timber be to be measured: measure the whole log as though it were not hollow, as above is declareth. Then measure the narrower and broader side of the hollow: and see what is contained in that, as though it were massy Timber. Now pull out the content of it, from the whole above measured: the remain of force must show what timber is included in that hollowed body. I Am unable in few words to express to the unlearned, by what mean Pyramidal, or picked regular steeples of all fashions are measured. Also how Pyllers: how the content of Globes or Bowls are searched: unless the art of numbringe were tasted. That being known: thus (as now followeth) I teach. How the Crassitude of picked steeples is known. MVltiply the plain of the Base in the third part of the height: so ye have the Crassitude. Or multiply the content superficial (found as I have instructed) in the height of the steeple, taking for your purpose the third part of that product. How the content of Pillars is known. Increase the base plain in his altitude or height: so have ye your desire. How the cubical bodies of Globes are searched. THe content superficial found (as I have opened) must be multiplied in the sixth part of the diameter: the product is that ye require. Or the third part of the Superficial content in half the diameter. Or multiple the plain of the Circle in the whole diameter: then take two third parts, which added make the crassitude. Of the half Circle. HIs superficial content multiplied (as is said) bringeth the magnitude of him. If any man require ensamples of this last matters, or more sufficient handling: let them resort unto my books published of geometry, there they shall be satisfied. These little apperteyn to Carpenters or Masons, therefore not by ensample declared. A general Note. WHen thou shalt be put to measure some body without order or fashion, lacking part of his square, or having more than his form: if it lack thou shall make it perfect by observing diligently the running together of the sides. The parts wanting shall be measured as though they were there, which portions must be taken from the whole body measured. Also when there resulteth any more than the form or regulare square: first measure the square body: then the crassitude which aboundeth. All put together do show the whole irregular body. This sufficeth. A table to find the just Radix or Square of any Timber, or Stone. IT behoveth you to know that this Table following is made for the true square of any manner Timber. Therefore understand that the numbers from .1. to .40. set above in the high margin betoken the Inches of the broader side of the timber. And the numbers from .1. and so downward to .30. put in the right part and hanging margin of this Table, signify the inches of the narrower side: and to conclude briefly, the elements or figures set in every square room betoken the just square. The bigger sigures leftwarde in every square place, signify the whole inches. And the other lesser ryghtewarde in the same square divided by a line, the parts of inches, as ½ ⅖ etc. This first fraction toward the left hand betokeneth one half part of an inch: tother two fyftes of an inch: and every figure or fraction, having a point adjoined unto him, somedeal less than the part is: as this part ½ representeth scant half an inch, a very little quantity less. And if he had two pricks by him, he should have declared some quantity more: as this other fraction or part: ⅖ which is more than two fifths, a small deal. It had not been needful to have put the parts of the square so precisely as they are here: neither is it requisite so curiously to take them. TABULA RADICUM. The Table of Squares 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1 1 3/7 1 ¾ 2 2 1/4 2 ½ 2 3/5 2 4/5 3 3 1/7 3 ⅓ 3 ½ 3 4/7 3 ¾ 3 7/8 4 4 1/8 4 1/4 4 ⅓ 4 ½ 4 3/5 4 6/9 4 ¾ 5. 5 5 1/10 5 3/16 5 ⅓ 5 2/5 5 ½ 5 ½ 5 5/8 5 ¾ 5 9/10 5 7/8 6 6 1/16 6 1/8 6 1/4 6 ⅓ 1 2 2 2/5 2 4/5 3 1/6 3 ½ 3 ¾ 4 4 1/4 4 ½ 4 2/3 5. 5 1/10 5 1/4 5 2/5 5 5/8 5 4/5 6 6 1/7 6 ⅓ 6 ½ 6 2/3 6 5/6 7. 7 1/16 7 3/14 7 3/8 7 ½ 7 3/5 7 ¾ 7 7/8 8 8 1/8 8 1/4 8 3/8 8 ½ 8 5/8 8 ¾ 8 7/8 9 2 3 3 ½ 3 6/7 4 1/4 4 5/8 5 5 4/5 5 ½ 5 ¾ 6 6 1/4 6 ½ 6 3/5 7 7 1/8 7 3/8 7 ½ 7 ¾ 8 8 1/8 8 5/16 8 ½ 8 2/3 8 7/8 9 9 1/6 9 ⅓ 9 ½ 9 2/3 9 4/5 10 10 2/10 10 1/4 10 2/5 10 ½ 10 5/7 10 4/5 11 3 4 4 ½ 5 5 1/4 5 2/3 6 6 ⅓ 6 2/3 7 7 1/5 7 ½ 7 ¾ 8 8 1/4 8 ½ 8 ¾ 9 9 1/6 9 ⅓ 9 ½ 9 ¾ 10 10 1/5 10 2/5 10 3/5 10 4/5 11 11 1/8 11 ⅓ 11 ½ 11 3/5 11 4/5 12 12 1/6 12 ⅓ 12 ½ 12 2/3 4 5 5 ½ 6 6 ⅓ 6 ¾ 7 1/14 7 3/7 7 ¾ 8 1/16 8 3/8 8 3/5 9 9 2/9 9 ½ 9 7/9 10 10 1/4 10 ½ 10 ¾ 11. 11 1/6 11 ⅓ 11 ½ 11 ¾ 12 ½4 12 1/4 12 ½ 12 2/3 12 4/5 13 ½6 13 2/9 13 3/8 13 ½ 13 4/5 14. 14 1/7 5 6 6 ½ 7. 7 ⅓ 7 ¾ 8 1/8 8 ½ 8 5/6 9 1/6 9 ½ 9 5/6 10 1/10 10 2/5 10 2/3 11 11 ●/4 11 ½ 11 ¾ 12 12 1/4 12 ½ 12 ¾ 13. 13 1/5 13 3/7 13 2/3 13 5/6 14 1/14 14 2/7 14 ½ 14 5/7 15. 15 1/10 15 ⅓ 15 ½ 6 7 7 ½ 8 8 3/8 8 4/5 9 1/6 9 5/9 9 8/9 10 1/4 10 3/5 10 9/10 11 1/6 11 ½ 11 6/7 12 1/8 12 2/5 12 2/3 13. 13 1/4 13 ½ 13 ¾ 14. 14 1/4 14 ½ 14 ¾ 15. 15 1/5 15 2/5 15 2/3 15 6/7 16 1/12 16 ⅓ 16 ½ 16 ¾ 7 8 8 ½ 9 9 ⅓ 9 4/5 10 1/5 10 3/5 11. 11 ⅓ 11 2/3 12 12 ⅓ 12 2/3 13. 13 1/4 13 ½ 13 5/6 14 1/7 14 3/7 14 2/3 15. 15 1/4 15 ½ 15 ¾ 16 16 1/4 16 ½ 16 ¾ 17. 17 1/5 17 3/7 17 3/5 17 6/7 8 9 9 ½ 10 10 2/5 10 4/5 11 1/4 11 3/5 12 12 3/8 12 ¾ 13 1/13 13 2/5 13 ¾ 14 1/16 14 ⅓ 14 5/7 15 15 1/4 15 2/3 15 7/8 16 1/7 16 2/5 16 ¾ 17. 17 1/4 17 ½ 17 ¾ 18 18 1/4 18 ●/2 18 ¾ 19 9 10 10 ½ 11 11 2/5 11 ¾ 12 1/4 12 2/3 13 1/32 13 3/8 13 4/5 14 1/8 14 ½ 14 6/7 15 1/6 15 ½ 15 4/5 16 1/8 16 2/5 16 ¾ 17 1/32 17 ⅓ 17 3/5 17 7/8 18 1/6 18 ½ 18 2/3 19 19 1/4 19 ½ 19 ¾ 20 10 11 11 ½ 12 12 5/12 12 ¾ 13 1/4 13 2/3 14 1/16 14 ½ 14 4/5 ● 3/16 15 ½ 15 6/7 16 1/4 16 3/5 16 7/8 17 1/4 17 ½ 17 6/7 18 1/6 18 ½ 18 ¾ 19 1/16 19 ⅓ 19 5/8 19 6/7 20 1/6 20 3/7 20 ¾ 21. 11 12 12 ½ 13. 13 2/5 13 4/5 14 2/7 14 5/7 15 1/10 15 ½ 15 6/7 16 1/4 16 5/8 17. 17 ⅓ 17 2/3 18. 18 ⅓ 18 2/3 19 19 1/4 19 2/3 19 8/9 20 1/5 20 ½ 20 4/5 21. 21 ⅓ 21 2/3 21 8/9 12 13 13 ½ 14. 14 3/7 14 5/6 15 ⅓ 15 ¾ 16 1/8 16 ½ 17. 17 1/4 17 3/5 18 1/32 18 3/8 18 ¾ 19 1/16 19 3/7 19 ¾ 20 1/16 20 2/5 20 ¾ 21 1/32 21 ⅓ 21 5/8 22. 22 1/5 22 ½ 22 ¾ 13 14 14 ½ 15. 15 2/5 15 7/8 16 5/16 16 ¾ 17 1/7 17 9/16 18. 18 ⅓ 18 ¾ 19 1/14 19 3/7 19 5/6 20 1/7 20 ½ 20 7/8 21 1/7 21 ½ 21 4/5 22 1/8 22 ½ 22 ¾ 23 1/16 23 3/8 23 5/8 14 15 15 ½ 16. 16 7/16 16 7/8 17 ⅓ 17 ¾ 18 1/6 18 3/5 19 19 3/8 19 ¾ 20 1/8 20 2/4 20 7/8 21 1/5 21 5/9 21 9/10 22 1/4 22 5/8 22 7/8 23 1/4 23 3/5 23 7/8 24 1/5 24 ½ 15 16 16 ½ 17. 17 3/7 17 7/8 18 ⅓ 18 7/9 19 1/6 19 5/8 20 20 2/5 20 4/5 21 1/6 21 ½ 21 7/8 22 1/4 22 5/8 23. 23 ⅓ 23 5/8 24 24 ⅓ 24 2/3 25. 25 1/4 16 17 17 ½ 18. 18 ⅓ 18 7/8 19 ⅓ 19 ¾ 20 1/6 20 5/8 21 1/32 21 2/5 21 5/6 22 1/5 22 3/5 23. 23 ⅓ 23 ¾ 24 1/32 24 3/7 24 ¾ 25 1/13 25 2/5 25 ¾ 26 1/16 17 18 18 ½ 19 19 2/5 19 7/8 20 ⅓ 20 ¾ 21 1/5 21 5/8 22 1/32 22 ½ 22 ¾ 23 1/4 23 5/8 24 24 3/8 24 ¾ 25 1/10 25 ½ 25 ¾ 26 1/7 26 ½ 26 ¾ 18 19 19 ½ 20. 20 ½ 20 9/10 21 ⅓ 21 ¾ 22 1/4 22 5/8 23 1/16 23 ½ 23 7/8 24 1/4 24 2/3 25 1/32 25 ⅓ 25 ¾ 26 1/7 26 ½ 26 7/8 27 1/5 27 ½ 19 20 20 ½ 21. 21 3/7 21 8/9 22 3/8 22 4/5 23 1/4 23 2/3 24 1/16 24 ½ 24 5/6 25 2/7 25 2/3 26 1/13 26 ½ 26 4/5 27 1/5 27 ½ 27 7/8 28 2/7 20 21 21 ½ 22. 22 ½ 22 7/8 23 ⅓ 23 4/5 24 1/4 24 2/3 25 1/10 25 ½ 25 8/9 26 ⅓ 26 ¾ 27 1/9 27 ½ 27 7/8 28 1/4 28 5/8 29. 21 22 22 ½ 23. 23 ½ 23 7/8 24 3/8 24 5/6 25 1/4 25 ¾ 26 1/8 26 ½ 27. 27 ⅓ 27 ¾ 28 1/7 28 ½ 28 7/8 29 1/4 29 5/8 22 23 23 ½ 24. 24 ½ 24 7/8 25 ⅓ 25 7/8 26 1/4 26 ¾ 27 1/8 27 ½ 28. 28 3/8 28 ¾ 29 1/6 29 3/5 30. 30 ⅓ 23 24 24 ½ 25. 25 ½ 25 7/8 26 3/8 26 4/5 27 1/4 27 ¾ 28 1/7 28 ½ 29. 29 1/8 29 4/5 30 1/5 30 3/5 31. 24 25 25 ½ 26. 26 ½ 26 7/8 27 3/8 27 4/5 28 1/4 28 ¾ 29 1/6 29 3/5 30 30 ⅓ 30 4/5 31 1/5 31 5/8 25 26 26 ½ 27. 27 2/5 27 4/5 28 3/8 28 ¾ 29 ⅓ 29 ¾ 30 1/7 30 ½ 31: 31 2/5 31 7/8 32 1/4 26 27 27 ½ 28. 28 ½ 28 7/8 29 2/5 29 4/5 30 1/4 30 ¾ 31 1/6 31 3/5 32 1/32 32 ½ 32 7/8 27 28 28 ½ 29. 29 ½ 29 7/8 30 ⅓ 30 7/8 31 1/4 31 ¾ 32 3/16 32 5/8 33 1/32 33 2/5 28 29 29 ½ 30. 30 ½ 30 7/8 31 3/8 31 7/8 32 5/16 32 ¾ 33 1/5 33 5/8 34 1/16 29 30 30 ½ 31 31 ½ 32. 32 3/8 32 7/8 33 ⅓ 33 ¾ 34 1/5 34 5/8 30 The table of Timber measure, with the declaration and use of it. THE, X. CHAPTER. THis Table (as ye see) is divided into two columns or rows: the one very short, the other longer. In the head of the first I have put this word Foot in the second row Inches and parts: to signify feet, inches, and parts of inches. The sums in the margin and left part of the first and second column, declare the quantity of the square of timber or stone, from .1. to 36. inches square. Within the rows you may find the just length to a foot square, if ye enter into them in right order, according to the square Ensample. suppose the square of your timber were .7. inches, and that ye desired to know what measure or length of the ruler would make a foot square. Seek in the lest margin .7. inches: and with him in that order toward the right hand, ye shall find 2. foot. 11. inches, & 2/7 of an inch. Note because the fraction 2/7. hath a prick by him, it betokeneth some small quantity less than 2/7 of an inch. If it had two pricks or points thus: 2/7 it should signify some little quantity more. Neither maketh it matter, whether ye observe this pricking or no, the quantity is so little to be added or pulled away. Note what hath been spoken of Timber, the same also is to be understand of stone, like wise to be measured. ¶ Thus is finished the measuring of timber, now ensueth of Board. etc. How Tables, Boards, Glass, or any such like are measured, according to their length and breadth only to the foot square. THE XI. CHAPTER. THis thing is performed by the help of a large table following, divided in six small tables, and as many margins The first and left marigne beginneth at. ¼. which is one quarter of an inch, and extendeth to .6. Inches, as ye may plainly perceive if ye run down by that margin. This hath his Table on the right side adjoining unto him. The other taketh his beginning at .6. inches. ¼. and endeth at .12. having his proper table also. The third, from .12 ¼ to .18. And so from .18 ¼. to .24. From .24 ¼. to .30 The last margin is from .30. 1/4 to .36, and there endeth. Of this that is said, you may gather that every margin hath his Table on his right side. Also you must know that in the top and beneath I have put (as in the table of Timber measure) these words, foot, inch, and parts, to signify feet, inches, and parts of an inch. Whensoever ye list to measure, Board, Glass, or any other such, with the breadth of it enter this Table: and seek that breadth in his proper margin. There ye shall find in right order how many feet, inches, or parts, of an Inch belong to a foot square. So often as the measure is in your stuff, just as many feet have ye in that board or such like. If the breadth exceed this Table: than divide the breadth in parts and work as is and shall be declared. So the ingenious applieth this Table for all manner breadthes most exactly. Ensample. SVypose I have a pane of Glass, or a board, whose breadth were 22. inches. ¼. the length .16. foot. In the fourth margin I find this breadth .22. and. ¼. And even with it in the Table rightward I see .6. inches. ⅓. So much of my ruler (wanting some small quantity) maketh a foot. Now, because in the length of my board (which is 16. foot) that measure is found .29. times, and. ⅔. parts. I concluded .29. foot there to be, & two third parts of a foot square, according to Foyes Thou Foyes Thou Thou Par Thou Par Thou Par Thou Par 1/4 48 6 1/4 1 11 ½5 12 1/4 11 ¾ 18 1/4 7 7/8 24 1/4 5 15/16 30 1/4 4 ¾ ½ 24 6 ½ 1 10 1/7 12 ½ 11 ½ 18 ½ 7 4/5 24 ½ 5 7/8 30 ½ 4 5/7 ¾ 16 6 ¾ 1 9 ⅓ 12 ¾ 11 2/7 18 ¾ 7 2/3 24 ¾ 5 4/5 30 ¾ 4 2/3 1 12 7 1 8 4/7 13 11 1/16 19 7 4/7 25 5 ¾ 31 4 5/8 1 1/4 9 7 1/5 7 1/4 1 7 7/8 13 1/4 10 7/8 19 1/4 7 ½ 25 1/4 5 2/3 31 1/4 4 5/8 1 ½ 8 7 ½ 1 7 1/5 13 ½ 10 2/3 19 ½ 7 3/8 25 ½ 5 5/8 31 ½ 4 4/7 1 ¾ 6 10 2/7 7 ¾ 1 6 4/7 13 ¾ 10 ½ 19 ¾ 7 2/7 25 ¾ 5 5/8 31 ¾ 4 ½ 2 6 8 1 6 14 10 2/7 20 7 1/5 26 5 ½ 32 4 ½ 2 1/4 5 4 8 1/4 1 5 3/7 14 1/4 10 3/32 20 1/4 7 1/8 26 1/4 5 ½ 32 1/4 4 ½ 2 ½ 4 9 3/5 8 ½ 1 4 15/16 14 ½ 9 7/8 20 ½ 7 1/32 26 ½ 5 3/7 32 ½ 4 3/7 2 ¾ 4 4 3/8 8 ¾ 1 4 3/● 14 ¾ 9 ¾ 20 ¾ 6 15/16 26 ¾ 5 3/8 32 ¾ 4 3/8 3 4 9 1 4 15 9 4/8 21. 6 ●/7 27 5 ⅓ 33 4 ⅓ 3 1/4 3 8 ⅓ 9 1/4 1 3 4/7 15 1/4 9 3/7 21 1/4 6 4/5 27 1/4 5 2/7 33 1/4 4 ⅓ 3 ½ 3 5 1/8 9 ½ 1 3 1/7 15 ½ 9 2/7 21 ½ 6 5/7 27 ½ 5 2/9 33 ½ 4 2/7 3 ¾ 3 2 2/5 9 ¾ 1 2 ¾ 15 ¾ 9 1/8 21 3/5 6 5/8 27 ¾ 5 1/5 33 ¾ 4 1/4 4 3 10 1 2 2/5 16 9 22 6 ½ 28 5 1/8 34 4 11/4 4 1/4 2 9 7/8 10 1/4 1 2 ½1 16 1/4 8 6/7 22 1/4 6 ½ 28 1/4 5 3/32 34 1/4 4 3/16 4 ½ 2 8 10 ½ 1 1 ¾ 16 ½ 8 ¾ 22 ½ 6 3/8 28 ½ 5 1/16 34 ½ 4 1/6 4 ¾ 2 6 ⅓ 10 ¾ 1 1 3/8 16 ¾ 8 5/8 22 ¾ 6 1/● 28 ¾ 5: 34 ¾ 4 1/8 5 2 4 4/5 11 1 1 1/11 17 8 ½ 23 6 1/4 29 5 35 4 1/8 5 1/4 2 3 3/7 11 1/● 1 4/5 17 1/4 8 ⅓ 23 1/4 6 1/5 29 1/4 4 7/8 35 1/4 4 3/32 5 ½ 2 2 1/5 11 ½ 1 ½● 17 ½ 8 1/5 23 ½ 6 1/8 29 ½ 4 7/8 35 ½ 4 1/16 5 ¾ 2 1 ½3 11 ¾ 1 2/7 17 ¾ 8 3/32 23 ¾ 6 1/16 29 ¾ 4 5/6 35 ¾ 4 1/32 6 2 12 1 18 8 24 6 30 4 4/5 36 4 Foe Thou Foyes Thou Thou Pa● Thou Pa● Thou Par Thou Par that length and breadth. I said (wanting some small quantity) because of the point joined to this fraction ⅔. which is put to diminish that fraction some little thing, as is declared plainly in the other tables before put forth. HE that desireth to measure Chamber floors, Pavimentes, or such like: let him only multiply the Breadth with the length: so the product showeth the content. Ensample. IF there were a Pavement. 100 foot long, and in Breadth. 50. I must needs conclude (by multiplication of that length in the breadth) there to be contained. 5000. foot. Or thus without Arithmetic when the breadth exceedeth the Table. Divide the breadth in parts (as is opened in the declaration of the Table of account) and work as I have before instructed. So for pavements all manner ways it serveth your turn. Of this matter to put for the tables, were superfluous tediousness and folly. The ingenious with these few, will be satisfied. The face of the Carpenter's ruler, figured with the true measures and other things necessary. THE XII. CHAPTER. BEcause the effect of this Ruler is above declared by Tables, an Instrument also well known and common among good artificers: I will not spend many words, in opening it. Behold the figures, and learn by them how ye ought to make, and commonly to deck your Ruler, both with Timber and board measure. Ensample. ADmit the ruler to be. a. b. c. d. well plained, twelve Inches long, a quarter of an Inch thick, and two Inches yn breadth. Truly it were more commodious, if it hath two foot in length. This ruler here imagined but a foot in length, is divided first in twelve even parts, called Inchess: then every Inch in half, or two equal portions: each half in two quarters: every quarter in four or two parts at the lest: as in this en sample. Then are the figures placed from. 1. to. 12. manifesting the inches. Thus your Ruler is ready to receive the measures which are marked or figured on your Ruler thus. And first the Timber measure as followeth. YE shall resort to your Table of Timber measure, and seek how many feet belong to. 1. Inch square: there ye shall find. 144. This number note write, or rather grave, where this figure. 1. representing one inch, is figured: as you may see in the mids between the line. e. f. and the line of the figure. g. h. This done. resort to your Table again, and behold how many foot and parts. 2. Inches square requireth. So shall ye find. 36. foot, which is placed in the next room leftwarde, under the charactere. 2. signifying two inches. Thus of the rest, feet, Inches, and parts, found in your Table, until you come to the. 12. Inch, where ye shall perceive. 12. Inches only to be set in his proper room. etc. Then seek further in your Table, what belongeth to. 13. Inches: Lo. 10. inches and. 1/5. This must be numbered in the line. c. a. from c which line betokeneth the thickness of the Ruler. Make there a little strike upon that grossness, even or right against the measure. 10. 1/ 5. what need many words. Thus do until ye come to. 36. Inches, and and that is noted (as the Table of Timber measure showeth (right with. 1. inch, and .3/3. from c. No otherwise is performed of board measure, as ye may behold set forth by the help of his proper Table in the square rooms, beneath the line. e. f. and also in the other thickness or line b. d. The back side of the Ruler, with the Quadrant Geometrical. THE XIII. CHAPTER. The backside of the ruler, Line of scaves. The line of heights upright. The making of a geometrical quadrant THis other figure. i k. l. m. is the backside of your Ruler, having in the mids a Geometrical quadrant. n. o. p. q. whose making in few words is thus expressed. The line or breadth of your ruler. n. o. the line. o. p. p. q. q. n. aught to be of one equal just length, cutting each other squirewyse. Note these three principal lines. Also from the centre. n. unto. p. is drawn an other line, which is called the line of height. So is. o. n. the line of level q. n. the Line of heights upright. This known, I open my compass, one foot remaining in the centre. n, the other extended in the line of level, almost to. o. making a Circumference unto. q. n. which is a portion of a Circle named a Quadrant: and aught to be divided into. 90. equal parts, as ye may behold every of them called a degree. Ye may divide the lines o. p. and. p. q. named the Scale, each in. The divided sides. o. p. & p. q. are called the Scale. 12. as here, or in. 60. yea, in. 100 equal portions is more meet, for the use of shadows, heights, lengths. etc. Note that the side or half Scale. o. p. is called the Contrary shadow: p. q. Right shadow. Remember that upon the thickness m. k. ye ought to have two fine equal square sights, well bored, represented here by r. s., made of wode, or rather metal, to be fastened there when time requireth. Let this satisfy. The common use of the Carpenter's Ruler, touching the face afore put forth. THE XIIII. CHAPTER. suppose a piece of Timber to be moaten, whose true square is. The .8. Chapter showeth how the true square is found 7. inches: this square appointeth you to the figure of. 7. in the line. g. h. under whom rightwarde in the place assigned to Timber measure, is written 2. foot. 11. inches, and. 2/7. As often as that measure is found in the length of your Timber, so many foot of Timber is in that piece. another Ensample. imagine your square to be. 22. inches: seek in the line. a. c. Note then how much of your Ruler is left from that, to the end of your Rule. c. and so much belongeth to a foot. Therefore lay out that measure upon your timber, and reckon how many times ye may find it, from the one to the other of your log: for so many foot of Timber is there. Even thus of Board. Seek the breadth upon your Ruler, in the room or place of board measure, and immediately before your eyes there remaineth what is to be laid out to make a just foot of board. The use of the principal lines in the Geometrical Quadrant on the backside of the Ruler, and first of the Level line. THE XV. CHAPTER. IT behoveth you to look thorough your sights. q. r. placed in the thickness or line. k. m. a fine thread and plummet falling at liberty out of the centre. n. If this plummet and thread chance precisely on the line of Leavel (which is. n. o.) whatsoever ye see thorough the sights, is level with your eye: if otherwise, the thing that ye look unto is not level, either more or less than the height or level of your eye: More if the plummet fall to youwarde: Less, if contrary. How by the line of Level to foresee whether the water of any springe or head is possible to be brought to a place appointed, and also to judge the wholesomeness of it. THE XVI. CHAPTER. YE shall go to the head or spring, and set your Ruler to your eye (being in height equal with the water) so the the fine cord and plummet fall precisely on the line of Leavell. Now if thorough the sights, ye may see above the place, know and judge the water possible to be brought, if your sight fall under, impossible. It cometh commonly to pass when the place to the which ye would have water conveyed, is of any great distance from the head, than hills, valleys, and such like impediments let the line vysuall to have his free course: wherefore this remedy is provided. At the head of the springe, ye shall look thorough the sights (as before) and note a mark in the next hill toward the place, then go to the mark: in like manner observe there an other in some hill: so forth until by any of them ye may perceive the place desired. If then your sight running through the pings of your ruler, (the thread ever falling on the line. n. o.) exceed that place, the conveying of your water is possible otherwise not. Now by the way briefly ye shall be instructed how ye may know the wholesomeness of water. TAke a clean pot and put water in it: How good water is known. so set it on the fire: after a little boiling, pour it out: if then no filthy remain in the bottom of the pot, it may be judged the houlsomer. Or thus. Let fall drops upon metel, or rather on glass (any of them being polished) and suffer that to dry by itself: if after there remain no spot or sign, it is a good token. Moreover, if your water be sweet, pure, clear, light, or of little weight, it followeth the water to be wholesome for the use of man. Of the line of Heigt. WHen so ever the thread and plummet do chance justly on the heigt which is n, p: the altitude or height that ye see is even with the distance from the Middle of your foot to the nether part directly under the top equal with your standing, adding the heigt of your eye downward, Know that ye must ever stand upright with body and neck, your feet just together, the one eye closed. etc. The line of upright Altitudes. judge also any thing plumb upright when the thickness of your Ruler. i l. is closely thereon, the plummet then at liberty, falling on. q. n, named the line of heights upright. Now followeth the use of the Scale. To search out heights by the Scale, with the aid of two places. THE XVIII. CHAPTER. LEt the thread and plummet fall in the one, on the .12. points: in tother station, on the .6. of the right shadow: double the distance between the two places, the summity appeareth from that part of the thing measured, which is equal in height with your eye. Or the one in the .12, the other in .8. of right shadow: then triple the distance. The one in the .12. the other in .6. of right, quaduplate the space. The one in the .12. the other in .6. of the contrary shadow, than the space between both the stations is equal with that ye measure, ever understanding from your eye upward. Even that same cometh to pass, if in the one the thread be found upon the .6. of the contrary, in the other one the .4. of the same. or the .4. and .3. of the contrary: In all thes the Spaces are equal with the altitudes. So then in measuring the distance between the two places, ye have the height, from your eye upward, putting to it the length from your sight downward, the whole Altitude appeareth: the base being equal with your standing. I Would not have you ignorant here how to know lengths which be in height not easy to come unto. first (as before) get the height of the top, the altitude of the base or longest part of your length. Subduct the less height out of the more, of force your desired length remaineth. How lenghts in height are known. Or thus: Let the plummet and thread fall in the .12. mark your place: go in toward the thing (the thread as it was) until ye see the base of that length: the distance between the two standings, is undoubtedly the length. How with the Scale, director upright heights, by their shadows are declared. THE XIX. CHAPTER. Turn your left side unto the Sun, suffering his beams to pierce both your sights. q. r. placed as afore is said in the thickness or line. k. l. The thread or plummet then hanging at liberty out of the Centre. n. showeth aswell the degrees of height to be counted from. o. as the parts of the Scale cut. If your thread be found in the .12. part, or line of level, shadows of all things being perpendicular elevated, are equal with their bodies. If the plummet with the thread be perceived cutting the parts next to the sights which I name points of the right shadow, than every thing direct is more than his shadow, by that proportion which .12. exceedeth the parts, where the thread was found. If it fall in .1. that is the first part of the right shadow, take the shadow twelve times to make the height. In two: that is the second part. Six times. In the third, four times. In the fourth, three times. In the fift, twice: and. ⅖. of the shadow. In the sixth, twice In the seventh once, and .5/7. In the eight once: and. ½. In the ninth once, and. ⅓. In the tenth once, and. ⅕. In the eleventh ye shall take the shadow once, and 1/11. part of it. Right shadow. If the art of numbering were had, I would will you to multiply the length of the shadow by .12. and the product divide by the parts, in the which ye found the thread. But and if it be in the parts of the contrary shadow, augment the length of the shadow with the parts declared by the plummet: and the increase divide by .12. so cometh the altitude also. Contrary shadow. Thus the composition and whole appliance of the Carpenter's ruler is showed: therefore somewhat shall be now said of the squire. I am not ignorant that the common use of him is better known than I can with many words express, wherefore I leave to write in that behalf. notwithstanding I will declare how heights, & Lenghtes are taken. etc. matters rare, and known of few Artificers. Also by tables to get a true knowledge of the day hour, and that divers ways, with the help of the squire: as is opened in my general Prognostication augmented in the year of our Lord. 1556. What length the sides of thy Squire ought to be, and the division of him. THE XX. CHAPTER. I need not to put forth the exact making of this Instrument so well known. Lo therefore thefygure. One side supposed two foot from the inward angle: and the other a just foot from the same. The longer. a b. inwardly divided from the angle▪ a. unto. b. into .24. equal principal parts, and every of them into a less (if ye list) each containing .10. minutes. Also the side. c. d. in the outward contrary plain from the top. c. unto. d is divided into .12. even portions: and again (if ye require exactness) every of them into .6. each of value .10. minutes. Behold a line & plummet falling from e. to f. a parallel to cd, and a. b. Thus this squire is well framed for the use of divers tables put forth in my general prognostication, & also for the finding of Altitudes and Longitudes, which here I purpose now briefly to open. How by this Squire heights are known. ALtitudes or heghtes are found, the line or plummet centred in the .6. point, cutting. h. the middle of. a. g. The movable sights placed in. a. g, or a parallel from that line, not unelike as is opened of the line of heigte, in the back of my ruler. How lengths in pleine ground are searched by the Carpenters or Mason's Squire. THE XXI. CHAPTER. TAke a staff divided into certain portions as ye list, in .100. or a. 1000 parts. At the beginning of your Length upon the very top directly standing: set the inward angle of the squire: lift up or put down this instrument untyle ye see the fardist part of your longitude. I mean until your sight running from that angle, to the end of your squire come unto the farthest part of that length. The squire so remaining, and the staff not removed from his height, mark where the other end of the squire next unto you noteh upon the ground. See what proportion the staff than beareth to the part of the ground, which the nearest end of the squire pointed unto from the staff, the same shall the Length have to the quantity of the said staff. Ensample. THe staff. The cause is taken out of Euclid. 32. pro. 1. book: and the. 4. pro. 6. book. a. c. in this figure is imagined .6. foot, & the space. a. d. 2. foot, Considering now that .6. the length of the staff conteinet .2. thrice, therefore the longitude desired. a. b. of force must contain three times the staff (which staff is .6. foot,) that maketh 18. foot. As this is proved true by a small ground in the figure following: so the art faileth not in a greater space, which the good speculator and diligent practiser by any way can not deny. Yet experience willeth me this to confess, that the squire is not convenient for any long distance, but the Instrument Geometrical (whose making and use ye may perceive in the treatise following) unless ye ascend some Tree or turret for your aid, which length known, shall stand in the stead of your staff. carpenter's square Carpenter's Squire. A Note. IT behoveth you to have a fine cord, made fast in the upper part of your staff. c. which shall be tied even with the inward edge of the squire, and so drawn to the ground, where the near end of the square from the staff pointed, as ye see. d. c. the other end then truly directing to the farthest distance. Know that the ground must be very plain and level, otherwise error ensueth. Thus the use of the Squire is here somewhat declared, but more in my general Prognostication, yea, most plentifully hereafter (God sparing life) in a book titled the rare use of the Squire in practices Mathematical: in the which book profitable pleasant experiences shall be plainly opened (only of me practised) as well of Perspective, as of the Mathematicals in general. I Had thought here following to have placed the ready handling of the compass, yea and to have showed the figuring and true making of all manner letters, both Text and roman, with the best proportion, the quantity as ye would demand, besides that, so to place them in height and nearer to the sight, that they being of divers magnitudes might appear to the eye, of one bigness. This when I did attempt to bring to their capacity, seemed somewhat dificulte without penning many words. Wherefore I omitted it, belonging rather to the Painter, then to the Carpenter for whose sake only the rest afore seemeth to be compiled. Here after (as I see men desireful) my endeavour may be to add that, and other things necessary. ¶ A little treatise declaring the making and use of an Instrument Geometrical (so far as it fardereth the Landemeter or Carpenter) named the profitable Staff. TO THE READER. I Said in the beginning that no little book would contain the making, and manifold fruits of this princely Instrument, if it were set forth as it ought to be. Certes the truth even here maketh me confess the same: He that desireth manifold fruits of this instrument, legate gen me fricii de radio astronomico, & geometrico, librum. yea, that there is no instrument so general and profitably pleasant. notwithstanding know (gentle reader) that the occasion of his chief use and profit is not here ministered: neither (to say the truth) doth it appertain to, or agree with the capacity of such Artificers. Therefore I shall leave to entreat of his ample large use, and best making, and will set him forth in few words: yea, sufficiently for the Landemeaters' capacity, or Carpenter's purpose, that at the least they may receive some kind of fruit with the Geometrer. And in time to come (by other means) as I see cause I will largely declare, and there deck him with his proper beauties. Here now followeth the making, and so briefly how he is applied for the profit of the afore named Artificers. The making of this profitable Rod or Staff. THE FIRST CHAPTER. YE shall prepare two small, straight, stiff, round, or rather square Rods, of metal or of wood well plained, of like bigness and length. Although it make no matter of what length, yet to avoid the errors, which little instruments and short staves bring, and also to bear with the rude unwonte handling of such Artificers: let your Rods be each five, or at the least three foot, and every foot divided in .12. even parts or inches, as ye see. a. b. &. c. d. These rods must be forged with a vice in the end of them to join readily .10. or .6. foot in length, (when time requireth) as the Figure e. f. showeth. Also ye must get (by the help of some craftsman. 4. other like rods, the longer g. 2 foot: the next. h .1. foot: the other. i. 6. inches: then k. 3. inches the last and shortest. l. 1. inch & ½. Each of these must have in their mids a hole, that the long staff of .10. foot may be put thorough them, & they moved on him at pleasure up & down, always cutting the longer staff. e. f. squyrewise, and made to tarry on any division as occasion shall be given: which all are easy to be perceived by the figures following, although my rude declaration hath not expressed my meaning. january hath xxxi. days Alramech. Oculus Tauri Alramech. For the night. 5 6 7 8 9 10 11 12 ♋ 1 108 123 143 165 190 213 59 79 From evening to midnight. 5 112 129 150 172 197 220 63 74 10 118 135 153 18● 2●6 227 68 78 15 123 214 156 192 ●1● 233 71 81 20 130 151 173 199 210 239 75 86 25 2●7 158 183 207 228 244 79 90 30 146 165 191 21● 23● 249 82 93 From midnight unto day 80 93 105 121 143 168 196 1 86 96 110 127 151 177 205 5 89 101 116 135 160 189 214 10 93 105 122 143 169 198 223 15 98 111 128 152 179 207 230 20 101 116 135 159 190 216 236 25 190 121 1●4 168 1●8 222 242 30 1 2 3 4 5 6 7 For the day. gr. ♒ 10 12 11 10 9 8 7 H Staff 36: 39: 49: 83: 550 0 shad. Squire 4: 4 3 2 0 0 shad. H 0 1 2 3 4 5 20 12 11 10 9 8 7 10 Staff 32 34 42 65: 209 0 shad. Squire 4 14 3 2 1 0 shad. H 0 1 2 3 4 5 30 12 11 10 9 8 7 20 Staff 27 29: 35: 52 119: 0 shad. Squire 5: 5 4 3 1 0 shad. H 0 1 2 3 4 5 February hath xxviii. days For the night. ●9 194 210 62 73 83 93 From evening to midnight. 5 174 199 222 64 75 86 98 10 84 207 228 68 79 90 1●2 Alramech. 1● 161 214 234 71 82 94 10● 10 198 220 238 75 86 98 111 Oculus Tauri 25 205 226 243 78 88 100 116 30 From midnight unto day 108 124 164 17● 201 225 1 111 129 153 180 207 231 5 117 136 162 190 216 237 10 122 144 169 198 223 243 15 128 152 178 206 230 248 20 134 159 188 214 236 252 25 Alramech. 30 1 2 3 4 5 6 For the day. gra ♓ 8 12 11 10 9 8 7 H Staff 2●: 25 30: 42: 80 6876 shad. Squire 6: 0 5 3 2 0 shad. H 0 1 2 3 4 5 18 12 11 10 6 8 7 0 Staff 20 21. 25. 34: 61 226 shad. Squire 7 7 6 4 2 1 shad. H 0 1 2 3 4 5 28 12 11 10 9 8 7 20 Staff 17 18: 22: 29: 45 112 shad. Squire 8: 8 6: 5 3 1 shad. H 0 1 2 3 4 5 March hath xxxi days. For the night. 5 59 70 81 93 105 120 From Evening to midnight. 10 62 74 84 95 108 125 15 65 76 87 99 113 131 20 69 80 91 103 118 138 25 72 83 94 107 123 146 30 75 86 98 112 129 153 30 90 102 117 135 161 From midnight unto day 142 168 196 222 241 1 147 173 201 227 245 5 157 183 210 232 250 10 163 192 218 238 255 15 171 200 225 243 259 20 180 208 232 249 262 25 Alramech. 191 216 237 254 267 30 1 2 3 4 5 6 For the day. gra ♈ 11 12 11 10 9 8 7 H 0 Staff 5 16. 19 24 37: 74: shad. Squire 9 9: 8. 6. 4. 2 shad. H 0 1 2 3 4 5 21 12 11 10 9 8 7 6 H 10 Staff 13 14 16. 21: 30. 54 22: shad. Squire ●1 10 9 7 5 2 1. shad. H 0 1 2 3 4 5 6 31 12 11 10 9 8 7 6 H 20 Staff 11: 12: 14. 18. 2●: 43 112 shad. Squire 12 12 10 8: 5: 3 1 shad. H 0 1 2 3 4 5 6 April hath. thirty. days. For the night. 8 9 10 11 12 1 92 104 118 138 164 From midnight unto day. 5 94 107 123 145 171 10 98 111 129 153 180 15 101 117 135 160 189 20 105 122 144 168 198 Alramech. 25 111 128 152 178 207 30 17 185 159 189 215 From evening to midnight. 103 210 229 255 1 Alramech. 99 ●25 244 258 5 207 231 248 262 10 215 236 253 266 15 223 253 157 70 20 230 248 262 274 25 236 252 266 278 30 1 2 3 4 5 For the day. gr. ♉ 10 12 11 10 9 8 7 6 H 0 Staff 10 11: 13 16. 23: 36: 76: shad. Squire 14 1: 11: 9: : 6: 4: 2: shad. H 0 1 2 3 4 5 6 21 12 11 10 9 8 7 6 10 Staff 9 9 11 15 21 31 48 207 shad. Squire 16 15 12. 9 7 4 2 1 shad. H 0 1 2 3 4 5 6 31 12 11 10 9 8 7 6 5 H 20 Staff 8: 28 10 14 19: 28 49 139 shad. Squire 18 17 14 10. 7: 5: 3: 1 shad. 0 1 2 3 4 5 6 7 NOW ENSVETHE THE needful necessary, peculiar Calendar tofore mentioned: with Instruments belonging thereto. The composition, and appliance of the said Table, with the pleasant use of them, are before sufficiently opened: therefore further declaration here, might seem superfluous. A necessary Instrument, to find exactly, the hour of the day, and night divers ways, With help of this Peculiar Kalendare. May hath. xxxi. days. For the night. 2 8 9 10 11 12 5 117 ●●3 160 190 2●6 From Evening to midnigt. 10 120 142 163 196 222 15 ●28 ●52 178 206 230 20 134 159 138 214 235 25 143 168 196 222 241 30 151 177 206 ●30 248 160 189 ●21 236 ●3● From midnight unto day 237 253 167 278 241 256 269 280 5 247 261 273 285 10 Alramech. 252 266 278 288 15 257 270 281 296 20 262 274 285 296 25 266 278 288 300 30 1 2 3 4 5 For the day. gra. ♊ 2 12 11 10 9 8 7 6 5 H 0 Staff 7 8. 10: 13 17: 26: 43 100LS shad. Squire 20 18: 15. 11. 8. 5 3 1 shad. H 0 1 2 3 4 5 6 7 22 12 11 10 9 8 7 6 5 4 H 10 Staff 77 9 11 17 24 39 82 25 80 shad. Squire 21 19 15 13 8 4 2. shad. H 0 1 2 3 4 5 6 7 8 32 12 11 10 9 8 7 6 5 H 20 Staff 6: 7: 9 12 16 2● ●7 78 56: shad. Squire 22 29 16 12 9 6 4 2 shad. H 0 1 2 3 4 5 6 7 june hath. thirty. days. For the night. 8 9 10 11 12 1 161 191 216 237 254 From evening to midnight. 5 169 197 223 242 257 10 180 207 231 249 262 15 191 216 237 254 267 20 199 224 243 258 271 25 207 231 249 262 275 Alramech. 30 216 237 254 297 379 From midnight unto day. 2●7 279 290 301 1 270 282 292 303 5 274 285 297 308 10 279 290 301 51 283 293 394 20 286 297 308 25 290 301 82 30 1 2 3 4 5 For the day. 1 12 11 10 9 8 7 6 5 4 H 20 gr. ♊ Staff 6: 7: 9: 12 16. 23: 37: 74 5●: shad. Squire 22 20 16: 12: 9: 6: 4: 2: shad. H 0 1 2 3 4 5 6 7 8 12 12 11 10 9 8 7 6 5 4 H 0 gr. ♋ Staff 6 7 9 12. 16 23 37 72 565 shad. Squire 22 20: 16. 12. 9 6 4 2 0 shad. H 0 1 2 3 4 5 6 7 8 23 12 11 10 9 8 7 6 5 4 H 10 Staff 6: 7 9: 12: 16: 23: 37: 74 565 shad. Squire 22 20 16 12. 9: 6: 4: 2 shad. 0 1 2 3 4 5 6 7 8 july hath. xxxi. days. For the night. 8 9 10 11 12 1 219 239 255 268 280 From evening to midnight. 5 225 244 250 272 253 10 233 250 264 275 286 15 238 254 297 279 290 20 243 258 271 283 293 Alramech. 25 249 262 275 286 297 30 254 267 279 290 300 From midnight unto day. 290 302 83 1 293 304 86 5 297 79 90 10 Alramech. 301 82 93 15 304 86 98 20 Oculus Tauri 308 89 101 25 82 93 106 30 1 2 3 4 5 For the day. 3 12 11 10 9 8 7 6 5 4 H 20 gr. ♋ Staff 7 7: 12: 16 24. 39: 82: 258: shad. Squire 21 19 15: 12: 8: 6: 4: 2: shad. H 0 1 2 3 4 5 6 7 8 14 12 11 10 9 8 7 6 5 H 0 gr. ♌ Staff 7 8 10. 13. 17 26 43 100 shad. Squire 20 18: 15. 11. 8 5 3 1 shad. H 0 1 2 3 4 5 6 7 24 12 11 10 9 8 8 7 6 5 H 10 Staff 8: 8 10: 14: 19: 28: 46: 139 shad. Squire 18 17 14 10. 7: 5: 3: 1 shad. H 0 1 2 3 4 5 6 7 August hath xxxi days. For the night. 8 9 10 11 12 1 255 257 279 291 302 From evening to midnight. Alramech. 5 250 272 284 294 304 10 203 275 286 297 79 Oculus Tauri 15 267 279 290 300 81 20 270 282 292 303 86 25 274 285 296 308 88 30 278 288 299 81 92 From midnight unto day. 82 94 107 122 141 1 86 98 111 126 146 5 89 102 116 132 154 10 93 105 119 138 160 15 96 110 125 144 167 20 Oculus Tauri 100 114 130 152 174 25 104 118 136 158 183 30 1 2 3 4 5 For the day. 3 12 11 10 9 8 7 6 5 H 20 gr. ♌ Staff 9 9: 11: 15 21. 31: 58: 207: shad. Squire 16 15 12: 9: 7: 4: 2: 0: shad. H 0 1 2 3 4 5 6 7 14 12 11 10 9 8 7 6 H 0 gr. ♍ Staff 10 11 13. 16. 23 36 76 shad. Squire 14 13: 11. 9 6 4 2 shad. H 1 2 3 4 5 6 24 12 11 10 9 8 7 6 H 10 Staff 11: 12 14: 18: 26: 43: 11: shad. Squire 22 12 10 8. 5: 3: 1: shad. 0 1 2 3 4 5 6 North. West. East. South. ❧ Thus is ended the Peculiar Calendar, very commodious for the day and night hour. I have here adjoined the Instrument without the Square, which may sufficie for the whole use of the t Calendar, with the help of the Squire and Staff. I May not here omit a Calendar general divided in two parts, whereof the first containeth six Months, from january to june: The second other six months from july to December. In this Calendar are setforth the Festival days, the entering of the Sun in the Signs celestial, the evil days noted with one Prick. For a further declaration of those evil days, read this following. The year hath xxxiii evil days general for ever. JANVARY hath eight such days, the i the ii the iiii. the .v. the ten the xu the xvii the xix Drink white wine this month. February hath three days, the viii the ten the xvii these not so evil, the xxvi. the xxvii the xxviii Eat no pottage of oaks or mallows: They are venomous. March three days. the xu the xvi. the xix this not so evil, the xxviii. day. This month, all sweet meats are good. April. two days the xvi the xxi these not so evil, the seven. the viii the x. the twenty Use hot meats, of light digestion. May three days, the vii the xu the twenty these not so evil, the three the vi Rise early, and use breakfast. june two, the four the vii: these not so evil, the ten the xi the xxii Sage & lettuce are good to eat. Cold water fasting hurteth not. july two days, the xu the .xx, abstain from earnality. August two days, the xix the twenty these not so evil, the first, the xxix, the xxx It hurteth not to abstain from pottage, and all hot meats and drinks of spicery. September two days, the vi the vii these not so evil, the iii the iiii. the xxi the xxii Eat good fruit. October one day, the vi: these not so evil, the iiii. the xvi. the. xxiiii God wine is olsome this month. November two days, the xu the xix: these not so evil. the .v. ●t the xxviii, the xxix bleed not. December three days, the vi the vii the ix thesedaiss not so evil, the xv the xvii the x xii. bleed not over much. Warm not thy legs at the fire. ¶ The first part of the general Calendar: from januarie to june. januarie. February. March. Days April. May. june. : A Circunci. d d 1 g b Phi. jac. e : b e Purifi. e 2 A c f c f f 3 b .d g : d g g 4 c c : A : c A A 5 d f b f Epiph. b b 6 e . g c g c c 7 . f : A : d A : d d 8 . g b e b e ☉ in ♓ f 9 A c f : c : f f 10 . b d . g d ☉ in ♒ g g ☉ in ♈ 11 c ☉ in ♉ e A Barna. e A A Spring. 12 d f ☉ in ♊ b ☉ in ♋ f Hilar. b b 13 e g c Summer. g c Valen. c 14 f A d : A d : d :A d :d 15 g : b . e b e : e 16 : A c f : c : f f 17 b d g d g g 18 c e A e A : A 19 d f b f b b 20 . e : g c g c c 21 : f A d A d d 22 g b . e b e e 23 A Georg. c f c f Ma. f 24 b d g joan bap. d Con. Pau. g g Ahun. 25 c Marc. e A e A A 26 d f b f . b b 27 e g c g c c 28 f A d : A d 29 g b e Pc. Pa. b e 30 A c f. c f 31 d ¶ The second part of the general Calendar: from julie to December. july. August. Sepemb. Days October. novem. Decem. g c Pet. Vin. f 1 A d Om. sam. f A d g 2 b e Om. ani. g b e . A 3 c f A c f . b 4 d g b d g c 5 e . A c e Dog beg. A : d 6 : f . b : d Nicol. f b : e 7 g c : e g c f Na. Ma. 8 A d f Con. ma. A d g 9 b e : g b e A 10 c f A c f b 11 d g b d g c 12 e A c ☉ in ♑ e A d 13 f b ☉ in ♐ d winter. f ☉ in ♌ b ☉ in ♍ e ☉ in ♎ 14 g ☉ in ♏ c e : g c f harvest. 15 A : d . f A d g 16 . b e g b e Dog end A 17 c f . A c f b 18 d Luc. g b d : g c 19 e : A c : e : A d 20 f b d f b . e Mathe. 21 g c e Tho. ap. g Ma. mag. c 22 A d f A d g 23 b e g b e Barho. A 24 c f A c jac. Apo. f b 25 d g b Na. do. d g c 26 e A c Steph. e A d 27 f b d Io. eud. f b e 28 g St. jud. c e Innocen. g c decol. Io. f Micha. 29 A .d f Tho. A .d g 30 b e Andre. g b e 31 c A Io the brief use of this general Calendar. ENtre the column where your month is noted in the head, ye shall there find running down the column the Festival days of that month, the entry of the Sun in the Celestial Signs, the Evil days pricked etc. I would have placed in this Kalendare the Fairs, Terms also, but that can not remain continual true: For those that ensue movable Feasts are movable, and therefore may have no certain place, For the Terms, note these precepts following The Fairs, shallbe declared by two Table immediately ensuing this Calendar general. How to know the Terms. KNow therefore, that Easter Term always beginneth the 18. day after Easter, reckoning Easter day for one: and endeth the Monday next after the Ascension day. Trinity Term heginneth the Friday next after Corpus Christi day: and endeth the Wednesday fortnight after. Michaelmas Term beginneth the 9 or 10 day of October: and endeth the 28 or 29 of November. Hilary Term beginneth the 23 or 24 day of january: and endeth the 12 or 13 day of Februarye, FINIS. General Fairs A Table containing the month, day, and Place of the principal Fairs of England: to be augmented at pleasure in order following january. The 6. day at Bristol, at Salisbery. The first of Lent at Exeter. February. The 2. day at Bathe, at Maydstone. The 14. at Feversame. Ash-wednesday, at lichfield, at Royston, at Tamworthe. The first monday in Lent, at Cisiter, at Abington. The 24. at Henlye upon. Thames, at Teukesbury. March. The 4. Sunday in Lent, at Stanforde, at Sudbery. The 5. Sunday at Grantam, at Salibury, the Monday before our Lady day at Wisbich Palm even The 13. at Wye. The 25. at Northampton, at Great Chart at Waulden. April. The 5. day at Walyngford. The 7. at Derby. The 9 at Byckelworth, at Bylling worth, at Easam the Mundy after The 3. Sunday after Easter at Louth. The 23. at Charing, at Ipswiche, at Amtill, at Hinigam, at Gilforde The 25. at Derby. The 26. at Tenterden. May. The 1. day at Stow the old, at Reading, at Maydstone, at Leiceter, at Chensford The 8. day at Beverly, ascension day, at Birmingcham, at S. Edes, at bishops Statforde. Withsondaye, at Kngstone upon Thames. Trinity sunday, at Rovel, at Cranbroke. The 19 day, the 27. day at Lenham. june. Corpus Christi. at Coventry, S. Edes, at Bishop Stanforth, at Rosse. The 9 at Maidstone. The 11. at Okingan. The 23. Shrowsbury, at S. Albon. The 24. at Cambridge, at Glocestre, at Lincoln, at Windsor Colchester. The 29. at Woller, at Hampton, at Peterborow. The 17 at Folkston. The 24 at Harisan. The 28. at Hetcorn. A Table containing the month, Day, and Place of the principal Fairs of England: to be augmented at pleasure in order following. july. The 11. day Horse fair at Partney at Nabor, at Felir. The 12. day at Lyd. The 15. at Pinchbacke. The 17. at Wynchecome. The 20. at Uxbridge, at Cattesby. The 22. at Marborow, at Winchester, at Colchester, at Tetbery The 25. at Bristol, at Dover at Chilham, at Ipswitch, at Northhampton, at Derby, at s james by London, at Reading, at Lowth, at Maelsbery. August. The 1. day at Feversame, at Donstable, at S. Edes, at Budforth at Marram Church, at Wysbyche. The 9 at Rumney. The 10. at Bedford, at Fernam, at Strodes, at Blakamore S. Lau. at Walton. The 24 at London, at Tewxsbery, at Sudberry, at Norwich, at Northalerton, at Dover, at Rye. The 28. at Ashforde. September. The 8. day at Cambridge, at Sturbridge, at London in Southwork, at Smide, at Recoluer, at Partney three Lady days. The 14 at Waltam abbey, at Wotton under Hedge, at Smaldinge. The 21 at Croyden, at Hulden in holderness, at S. edmond's berry, at Maulton, at S. jews, at Haldy Lanam, at Wyltemal, at Sittingborowe, at Dover, at Estrie. The 29 day at Canterbury. October. The 6 day at S. Scythes beside Norwitche. The 13 at graves end, at Windsor, at Marchefelde. The 18 at Elye, at Staneton, at Charing. The 28 at Harford, at Ciciter, at Newmarket. November The 2 day at Kingston, at Blechinglye. The 6 at Newporte pond, at Standly. The 11 at Dover. The 13 at S. edmond's berry The 20 at Hyth. The 23 at sandwich. The 30 at Rochester, at Maidenhead. Decē●●● The 29 at Canterbury. The 5 at Pluckley. The 6. at Spalding. The 7 at Sanderst. BEcause I understand many are desirous how to get exexactly the just length of Staff and squire shadow before treated of, upon unleavell grounds, or other ways where so ever it be, yea without ather squire or Staff. I have calculated a Table following, thoroughly satisfying them, so the they get the height of the Sun any way, or as I shall now instruct. Behold this Instrument called a Quadrant the just fourth part of a Circle. even such a Circle as I taught you before to make for the night Dial: containing the fourth part of his divisions, that is 90 degrees, only two sights and a plume line added, to be placed at the beginning of this book as ye may there: and here see. I have here also put the Scale to the Quadrant, which serveth well for shadows, and as well for heyghtes. the use of this Scale is declared in my book called Tectonicon. How by this Instrument to get the height of the Sun at all times. Let up handsomely your Quadrant the Sun beams piercing the sights. The plummet and Line then at liberty falling, noteth there the degrees of height at that present, with the which shall enter this Table immediatle following, to get them, and in like manner at all other times the just shadow of the Stue or squire. A Table general of Shadows, right and contrary for every grave of the suns height: The thing causing Shadow, supposed .12 parts. Height of the Sun. Staff. Shadow. height of the Sun. Staff. shadow. height of the sun. Staff. shadow. G g P M G G P M G g P M 0 90 Sha m. 30 60 20 47 60 30 6 56 1 89 687 34 31 59 19 58 61 29 6 39 2 88 343 43 32 58 19 12 62 28 6 23 3 87 228 59 33 57 18 29 63 27 6 7 4 86 171 37 34 56 17 47 64 26 5 51 5 85 137 10 35 55 17 8 65 25 5 36 6 84 114 0 36 54 16 30 66 24 5 21 7 83 97 49 37 53 15 52 67 23 5 6 8 82 85 28 38 52 15 21 68 22 4 51 9 81 75 46 39 51 14 49 69 21 4 36 10 80 68 3 40 50 14 18 70 20 4 22 11 79 61 44 41 49 13 48 71 19 4 8 12 78 56 27 42 48 13 20 72 18 3 54 13 77 51 59 43 47 12 52 73 17 3 40 14 76 48 8 44 46 12 26 74 10 3 26 15 75 44 47 45 45 12 0 75 15 3 13 16 74 41 51 46 44 11 35 76 14 3 0 17 73 39 15 47 43 11 11 77 13 2 46 18 72 36 54 48 42 10 48 78 12 2 32 19 71 34 51 49 41 10 26 79 11 2 20 20 70 32 58 50 40 10 4 80 10 2 7 21 69 31 16 51 39 9 43 81 9 1 54 22 68 29 42 52 38 9 22 82 8 1 41 23 67 28 16 53 37 9 3 83 7 1 28 24 66 26 57 54 36 8 43 84 6 1 16 25 65 25 44 55 35 8 24 85 5 1 26 64 24 37 56 34 8 6 86 4 0 50 27 63 23 33 57 33 7 48 87 3 0 38 28 62 22 34 58 32 7 30 88 2 0 25 29 61 21 40 59 31 7 13 89 1 0 12 30 60 20 47 60 30 6 56 90 0 0 0 Height of the Sune. squire. Shadow Heyht of the Sun squire. Shadow. Height of the Sune. squire. Shadow. The use of this Table, and first for Staff Shadow Ensample: I Suppose the height of the sun taken by the Quadrant 34 degrees, now I require the exact length of Staff and squire shadow. For right shadow, first seek out the degrees in the left part of the Table and under this title the height of the Sun: if they be not in that left row downwards, resort to the next row and like title, until ye find the degrees, then in right order toward the right hand, in the next column under the title of Staff Shadow, are 17 parts and 47 minutes, your desire. For squire shadow, titled contrary Shadow. Seek your degrees in the right part upward at this title Height of the sun, in the bottom of this Table: then shall ye find on the right hand of 34 degrees, in the next Columpn 8 parts and 6 Minutes: that is the very length of squire shadow, when the Sun is 34 degrees in height. OCcasioned I cannot here omit an other Table faithfully supputated for the suns altitude, by the which with quick speed the hour is known. This Table conducteth manifold ways, yea to the Composition of divers and many Instruments: as Quadrauntes, Navicles, Cylindres. rings. etc. Behold now it doth ensue, and also the brief use of it. A Table of the suns altitude for every hou● Pole mounted. 51. degrees 30. Minutes, exactly calculated. Hours before n. 12 11 10 9 8 7 6 5 4 Hours after n. 1 2 3 4 5 6 7 8 Si. G S G g M G M g M g M g M g M g M g M g M 30 ♋ 0 62 0 59 45: 53 45 45 42 36 42: 27: 23: 18 11 9 28: 1 31. 25 5 61 54 20 10 61 37: 59 21. 53 26: 45 24 36 25 27 6 17 50. 9 9 1 13: 15 15 61 9: 10 20 00 30: 53. 17 52 23. 44 32 35 35 25 16. 17 3 8 16. 0 16: 5 25 59 41: ♊ 0 ♌ 0 58 42: 56 34 50 55: 43 6. 34 13. 24 56: 15 41: 6 10. 0 0 25 5 57 34: 20 10 56 17: 54 15 48 48 41 10: 32 22. 23 6. 13 50 4 55: 0 0 1 25 51 43: ♉ 0 ♍ 0 50 0 48 11. 43 11. 39 53 27 27 8 13 8 5●: 0 0 25 5 48 21: 20 10 46 20: 44 37 39 51 32 53: 24 32. 15 27. 6. 8. 0 0 15 15 44 25: 10 20 42 23: 40 51: 36 18 2● 34: 21 24: 12 25: 3 6. 0 5 25 40 29: ♈ 0 ♎ 0 38 3● 36 58 32 37. 26 7: 18 ● 9 16. 0 0 25 5 36 30 20 10 34 32 33 4 28 55: 22 38: 1● 51: 6 7 0 0 15 15 32 35. 10 10 30 40. 29 16. 25 18 19 14 11 33 3 ●: 0 5 25 28 48 ♓ 0 ♏ 0 27 0 25 40 21 51: 15 59: 8 34. 0 6. 25 5 25 17. 20 10 23 39 22 22. 18 42: 13 1: 5 45. 0 15 15 22 8. 10 20 20 43. 19 29 15 55. 10 23: 3 19 0 5 25 19 26 0 ♒ 0 ♐ 0 18 18. 17 6 13 38: 8 13: 1 15. 0 25 5 17. 19 20 10 15 30 14 48. 11 55. 6 36: 0 0 15 15 15 51 10 20 15 23. 14 13 10 52 5 36 0 5 25 15 6 ♑ 0 0 15 0 13 51 10 30. 5 15. When the Sun cutteth the 22 grave of ♋ he toucheth our Horizonat 4 in the morning Entering the 22 of ♑ he riseth at 8 in the first of ♉ at 5. in the first of ♍, at. 7. Note in all my tables, one prick following the Minutes, diminisheth: two, augmenteth some small quantity