TECTONICON:

BRIEFLY SHEWING

The exact meafuring, and speedy reckoning
all manner of Land, Squares, Timber, Stone, Stee-
ples, Pillers, Globes, &c. Furthermore declaring
the perfect making and large use of the Carpenters Ruler,
containing a Quadrant Geometricall comprehending alfo
the rare use of the Squire. And in the end a little Treatife adjoyning,
opening the composition and appliancy of an Instrument called
the Profitable Staffe : With other things pleasant and neceffa-
ry, most conducible for Surveyers, Land-meeters, Joy-
ners, Carpenters, and Masons.

Published by LEONARD DIGGES Gentleman, in
the year of our Lord, 1556.

25 Dic. 32 7 is the length of a, a.

LONDON,

Printed by Ric. Hodgkinsonne, and are to be sold by
Nath. Brooks, at the Angell in Cornhill, 1656.

The pleasant Profit or Content of this little Book, and
in what it exceedeth all other published

Ther Books before 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 of
Land, Timber, Stone, Steeples, Pillers, Globes, Board, Glasse,
Pavement, &c. without any trouble: not painted with many rules,
or obscure termes, nor yet with the multitude of tables, as here-
tofore hath been: in which not a few errors were committed: for
that cause no juſt account might any way bee had. Further yee
ſhall by this Book understand the whole making and comely
handling of the Carpenters Ruler, with the true meaſure, &c.
And his use appointed to the ready meaſuring of all kindes of Tim-
ber, Stone, Board, &c. Also the levelling of grounds, and taking
of heights, is pleasantly and diversely prætised by the Ruler. Yee
have here not the common, but the rare use of the Square, applied
to heights, lengths, &c. And to the finding of the juſt houre of the
day divers waies, through the aid of pleant Tables newly ad-
joyned to my generall Prognolification: by the which the pro-
portion of things, direct or ſquirewife standing, are by their ſha-
dowes known.

To conclude, in the end of this Book is added a Treatise,
Chewing the making, and use of an Instrument, by which yee
will get lengths, heights, breadth, widenesses, where
or howleever they stand. Other necessary things
are contained in this little volume, which I
commit to the diligent
READER.

Divers

Divers things conducible to the Art
of meaſuring.

The i. Chapter.

As there are ſew Craftmen which have
all the kindes of Arithmetick readily:
so I doe ſuppose none so ignoant, but
that they doe or may easilie perceive the
simple ſignifications of these Characters
or Figures, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
And also their strength in the first, ſe-
cond, and third roomes placed.

Characters
num:all.

Besides that they must be familiar with these and such
like Fractions.

The first leftward betokneth one second part of an whole, be it Pearch, Inch, or any other meaſure: the next one third, then one seventh part; the other enluing one twelfth. 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 poztions.

Fractions.

These I doe intend to put in my examples, and in my
Tables and margins following, to represent parts of Pear-
ches or Inches. As if I would write half an Inch, after
this

A 3

this

The Art of

this manner. Thjſe quarters of an inch thus divided eight of a Pearch, on this wifh. So of this reſt.

It is requisite also here to open what a Pearch, a Day, work, a Rod, and an Acre is.

Although there be divers opinions engendered through long cuttome in many places, of the length of a pearch (upon which our chief matter dependeth) yet there is but one true pearch by Statute appointed to measure by. Wherein is oſdained this Barly coths dry and round to make an Arch: twelve Anches, a Foot: this foot a Pard: five Pards, a Pearch: foſtie Parches in length and four in breadth, an Acre. So an Acre by Statute ought to contain 160. Parches: the half Acre 80. Parches: a Rod, commonly called a quarter, 40. Parches: a Day, work 4 Parches. Loe here the Acre erpelled with his length and breadth.

I must not omit here to tell you what thing is meet to measure land with. They use commonly in the Country two Poles, either of them the length of a Parch. They are very good: yet foz all kind of lands, a Cord five Parches in length, well leared with war and rosin, knotted oſ marked at the end of every Parch, is moſt meet and readeſer. But in my ſantastic, the Instrument Geometricall, which is put foſth in the end of this Book, palfeth them all and other, foz the exact truth and quickett ſpoe; this Instrument is ſo generall and abileable to ſo ſundry things, that it alone requireth a large book, if it should be ſufficiently ſet foſth.

Also I would not have you ignoſant what peice of land is called a Triangle, which often hereafter shall be named. It is ſuch a ſaſhoned piece as hath (oſ is imagined to have) this ſides, and this Angles only: whether the ſides be equal or otherwise, as this figure doeth. Again, note that a lins is ſaid to fall Squirewise when it cutteth any thing or any of a Triangle full crosſe, like unto a Squire. As the Hanging pricked

Acre.

Instruments to
measure with
Poles.
Cord knotted.
Profitable
Staffe.

Triangle.

Line falling
Squirewise.

meaſuring of Land.

2

pricked line a. b. in c. d. the base line of the Triangle. Loe it cutteth the ſide Squirewise, oſ full crosſe in the point b. and not as the other line a. c. doth. The base of any triangle is here called that ſide, which is cut Squirewise of the hanging line.

Concerning a Circle, know that the compals of any Circle is named a circumference: the middle point in him, his Center: the right line h. i. that goeth overwhat that Center touching the circumference on both ſides is his Diameter: the half of that line, the Semidiameter. Also an Arch is a peice of the Circumference cut away: as ye see the Arch above the line f. g. Also f. g. h. i. in this Circle are named parallels: foſ that they differ equally in all places, the one from the other.

Note, because practice and experience doeth me, that there is almost no land, but it may easily be brought by imagination to a triangle of triangles, and so most truly measured: therefore, to be exact, this order shall be taken: I will first figure and set before your eyes triangulated land, and other which by imaginations shall be brought into triangles. Then I shall teach the true measuring of them: I mean, how to find a length and breadth, with which I shall enter the table of account following, where the Acres and odd Parches (if there be any) shall appear. As these figures are measured, so all triangulated lands, and other brought into Triangles, of what fashion so ever they be, shall be measured. And because it is requisite that true measuring of all Triangles, to find a straight hanging line, I shall show you how that line is to be found, imagined, or drawn.

How.

Base line.

Circle.
Circumference.
Center.

Diameter.
Semidiameter.

Arch.

Parallels.

## 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 bisawn or imagined from any Angle, cut-
ting some one side of that Triangle Squire-
wife; as we may perceive the pricked lines in
the Triangles following. By the helps of
this line, all lands of triangle fashion, are
brought to be measured as enlueth.

How

## measuring of Land.

### How to measure all manner of
triangled Land.

The iii. Chapter.

If thou be an Arithmetician, multiply this
freight hanging line, bisawn, as above is then-
ed, in half the number of Parches of that side,
which it cutteth squirewise. For want of the
knowledge, take the aforenamed Parches (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, Rods, Pay, Wozks.

### Example.

For the perfect measuring of Triangles afore figured, and all other, suppose the second of these last nine figures of the other side, having written above it a, b, c, d, to be a piece of land, whereof I would have the true measure, I finde by a cord, otherwise, the pricked hanging line a, b, to be 23. Parches: the side b, c, which it cutteth squirewise 44. Parches, whose half is 22. With these 2 and 23. the convenient length and breadth, I enter the table of account. There I finde by that table at the corner where both the lines of convenient length and breadth do meet: 3 Acres, 6 Pay, Wozks, and two Parches to be in that Triangle. Thus of all before figured.

Here note your table must ever be entred with all the Parches of the hanging line, and with half the side that he cutteth squirewise. For with the half hanging line, and the whole side cut.

This Table
follower.

B

A Figure

The Art of

A figure of a double Triangle.

This figure e. f. g. h. is but two Triangles : and therefore measured as above in two parts. Di thus : The hanging line e. g. is 33. Parches : the side f. h. that he cutteth Squirewise 20. Parches, the half of the which is 10. Now enter your table as before with 33. and 10 the convenient length and breadth. So shall yee finde two Acres, two Dayworks, and two Parches, the true content of this figure e. f. g. h.

Another Example.

Figures of ma-
ny Angles.

Amit i. k. l. m. land to be measured. Because it is no manner triangle, it must be brought by imagination, as I have said, into a triangle or triangles. Which imagination is here signified by the line dathen i. l. Then as above is declared,

it ought to be measured (according to the rule of triangles) in two parts, because there are two triangles in that land. So by proof yee shall have in the upper i. m. l. one acre, 3. Roods, and five Day works; in the other i. k. l. one acre. Thus I gather the whole content of that land to be two acres, three Roods, and five Day works.

None

measuring of Land.

4

None otherwise of the adjoyned, n. o. p. q. and all other figures following : and other whatsoever they are, that by any means may be brought into triangles.

Furthermoze know that the figure i. k. l. m. is readily thus measured. Add the parches of both the hanging lines together, so have ye 33. With this number, and with half the parches of the side 1. which he cutteth Squirewise, being 10. Parches, enter your table. So is found as above.

These two figures following may also be thus measured, otherwise then by the rule of Triangles. Enter your table with their convenient length and breadth. So shall you finde the contents of all such.

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 ennueth.

Lay together the two sides which are parallels of the first figure a that is 6. & 18. making 4 the half is 12. the breadth 5. Enter with 5. and 12. your table. So have you one rood, and 5. day works. For the other two b. c. and such like, join the heads of ends in one; and enter your table with half of those parches, and with the whole number of the middle line.

In
me
Pol
Co
Pro
Sta

Tr.
Lix
Sq.

The Art of

Example.

Suppose a piece of land, whereof the compals is 100. Peares
ches, the breadth 32. Parches. I would know how much
land is in this figure. Enter your table with half the com-
pals, that is 50, and with half the
broadth, that is 16. Parches. Because
in the Table I cannot find 50 foz the
greatest length is 40. (therefore I en-
ter with 40. and 16. So is found foure
Acres. Then I enter again with 16.
Parches remaining, and 16. the breadth
as before, that bringing 1. Acre. Now
to conclude my addition of 1. and 4. I find five Acres in that
round land, whose half compals is 50. Parches, and the
broadth 16. Parches.

How parts of Parches are to be
counted in measuring.

EDZ perfect knowledge and use of this Table following,
when parts of Parches are adjoyned, note well this other
erample that enfueth, and also what is said of the declaration
annered unto the Table, when
parts of Parches are in the
length, breadth, oz both.

Imagine f. g. h. to be a round
piece of land : I find by mea-
sure the whole compals, 99.
Parches. The half is 49.
The hanging Line oz half
broadth is 15 1/2. Enter your
Table with the whole Pear-
ches, that is 49. and 15. lead
ing out 1/2. and 1/4 which were but parts of Parches. So have

Yee

measuring of Land.

Yee 4. Acres, 2. Rods, 3. Day, works, and 2. Parches. For those parts of Parches omitted, at your first entering the Table, work thus. The half Parch, quarter, oz other part of a Parch in the length, must be reckoned by them. selves in the whole breadth, and those of the breadth contrary, wife 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, joyning to the other afore got. ten, remembering the product of the one fraction multiplied in the other, to be pulled from the increase. To make this matter plain, I will take this last example before. The one number wherewith I should have entered my table, was 49 1/2. the other 15 1/2. I found first by entering with 49 1/15. (omitting the odd parts) 4. Acres, 2. Rods, 3. Day, works, and 3. Parches. Now for the increase of the parts of Parches left out, I must (as I said) reckon them of the length in the breadth, and contrarily wile them of the breadth in the length. Half 15 1/2. is 7. Parches, and 7/2. Three quarters of 49 is 37. Parches 1/2. which added makes 45. Parches. This adjoyned to the number aforegotten, bringingeth to the whole content of the round figure, which is 4. Acres, 3. Rods 4. Day, works, 3. Parches, and 1/2. of a Parch, the product of the one fraction multiplied in the other subordinated. What must be done when the numbers wherewith yee should enter, created your table; counsell the declaration of your table there adjoyned.

Of the half Circle.

EDZ this half Circle, enter the
table with half the compasse,
and with half the Diameter of
the Circle, oz with the length
of the pricked hanging Line, k. 1.
So the content of this half Circle
is 2. Acres, 1. Rod 7. Day,
worker, 1. Parch, and 1/2. of a Parch.

To measure
half circled
Land.

Another

In
me
Po
Co
Pr
St

T
Li
S

6

# The Art of measuring

Or thus by the rule of proportion, the parts of a Globe are found.

To measure
parts of Globes

S uppose a. b. c. to be a piece of a Globe, and 4. to be a proportion of the Diameter, the whole being 14. Thus I say, 14. the whole Diameter gives 616. the content superficial of the 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 D:-
measure of a
Globe.

I f ye be ignozant what length the diameter of the Globe is, whose proportion ye have, the height or part of the Demetius being 4. foot, augment half the line a. b. which is 6 1/2 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.

Erst ye shall measure the circuit of the foot, or base of the Mountain: then the compals of the summity or top, adding them together. So shall ye doe of the ascenses, that is, the going up from the foot to the top, joyning the measure of the longer and shorter in one. Now take the half of the circuit added, and the half part of the ascenses joyned, and enter your table: there shall ye see the content.

Enfample

# Mountains and Valleys.

9

Enfample.

A. b. c. is the mountain: a. c. the circuit of the Base, being 100 Parches, or the top 16. Parches. Which joyned together,

make 116. b. c. the one ascense is 55 Parches: the other 75. These added make 120. The half of the circuits is 58. the half of the ascenses 65. with these two summes ye shall enter your table of account,

where ye shall find 23 Acres, 2. Hows, and 10. Parches, the true content of this figured hill.

Figure of a
Mountain.

## Of the Valley.

A s in the Mountain ye measured the circuit or compals of the Base or foot; so here contrary ye shall meet round about the circuit or compals of the height of the Valley. And as ye got the measure or compals of the top of the Mountain, so measure the circuit of the depth of the Valley. In like manner as ye measured the ascense, that is, the going up from the foot to the top: so measure the descent or going down of the Hill to the depth of the Valley. The rest all work, as I have showed you in measuring the Mountain.

For more plains, behold this enfample or figure. If ye lay together the circuits of the height and depth, which is 210. and 20. taking

the half part of those two circuits, making an 120. then the

To measure
Valleys.

Figure of a
Valley.

## The Art of measuring

the two ascensens 140. and 60. added in one product 200. the half thereof being 100. with this and 120 the other half of the Circuit, ye may enter your table. That doing, loe 75. Acres.

### How the Table of account now following is to be used.

What is to be done when numbers, with which you should enter, exceed your Table.

When you have gotten a convenient length and breadth, (as I have above declared by divers triangles and other figures) then you shall enter this table. Seek there the length, and most number of Parches in the higher margine, which beginneth at 1. and endeth rightward at 40. Look the other sum of Parches (I mean the breadth) in the right side and hanging margine; from 1. descending to 30. Now at the meeting of the line, where the one answereth the other directly in a square, you shall find the Acres, Rods, Day-works, and Parches. Note that the first number set on the left side, and upper part in any square, signifies the number of Acres. The figure 1. set in the upper part, and right side, doth betoken a Rod: the figure 2. there two Rods: 3. three Rods: And the figure in the left side beneath, signifies a Day-worke, or Day-works. A figure in the lower part rightward, declares Parches.

### A Declaration adjoyned.

When it chanceeth that the one number or both, with the which ye should enter this table, are greater then any here found; it behoveth you to take the half of the one, and the whole of the other, or what parts ye like 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.

Enfample.

## Mountains and Valleyes.

### Enfample.

Suppose the number with the which ye should enter your table to be 130 Parches in length, and the breadth 60. neither of these may be found in the margine: wherefore I take the third part of an 130. which is 43. Parches, and one remaineth.

The half 60. that is 30. I find with entring them at the common meeting 6. Acres, 1. Rod, and 5. Day-works. This summe 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 first, which signifies that ye have found by entering but the sixth part of the number ye should find. Therefor I must take this summe also found (being 6. Acres, 1. Rod, and 5. Day-works) six times as much. So have ye 33. Acres, and one Rod. For the Parch remaining in length, reckon him in the breadth (as is also declared) in the fifth Chapter of the remains: so have ye 60. Parches more to be added. So the increase of these two numbers 103. and 60. amount to 38. Acres, two Rods, and five Day-works. Thus any manner length and breadth is reduced to this table following, which sufficeth.

Thus with few words is ended the certain measuring of all manner of Land, touching the superficial content. Wherefore now shall follow the true measuring of Timber, Stone, Stumples, Pillers, Globes, according to their Crats, Skitude.

Such as are altogether ignorant of Aritmetick, may remember by our English cogn, allowing so every Parch in length or breadth a Penny, and so every Mark makes an Acre, every Noble half an Acre, every fourth Pence or half Noble a Rod, and every Penny a square Parch. And so by memory without tables, may in some rude and gross manner, take up reasonable just the true contents of all Cloves, Medowes, Marshes, Hils, or Valleyes.

Look what I have shewed in the Chapter of part I, that understand here of whole Parches, left subtracting &c.

C 3

To

To the Reader.

In a foot
square is con-
ained 172.
inches.

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 you must handle all such fashioned Timber (as afore
is spoken of) there shall follow a Table in which ye may finde (as
I will declare) the square of any Stone or Timber. That known,
it is requisite to have another 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. With the length agreeable to
your Square, your Log must be measured. And as oft as ye finde
it from the one end to the other of your Timber, so oft you may
conclude the foot square to be contained in that Timber, Logge,
or Stone: that is, so many square Feet there to be included. This
Table of Timber-measure standeth in the place of a good
Ruler, well decked with true measures. By
this ye may make or correct Ru-
lers at pleasure, as after
appeareth.

Now orderly followeth the true measuring of all fashioned
Timber or Stone aforenamed.

How Timber or Stone four square every
way, or broader on the one side than on
the other, is measured.

The vii, Chapter.

If a piece of Timber or Stone, be either
equally square, bzoaver on the one side
than on the other, yee shall take the just
measure, a mean, how many inches
the bzoaver lde containeth: even so of
the narrower. This done, yee must take
in the table of Squares following, the
measure of the bzoaver lde of the Tim-
er or Stone, in the upper margine of that table. When look
at the number of inches, of the equall or narrower side, in the
right part and hanging margine. At the common meeting
where the one number answereth directly to the other, there
is true square shall appear. This square so found, shall
referred to your table of timber measure: in the which you
will plainly see (if you runne down by the left margine, untill
our inches square appear) how many feet or inches of your
timer belong to a foot square. As often as that measure there
is, is contained in the Timber or Stone, so often and as
many feet square ye may conclude (without doubt) the piece of
Timber or Stone to have.

D

Enfample.

The Art of measuring

Ensample.

Suppose this squared Timber of Stone a. b. c. d. were to
be measured, the bzoader side a. b. 20 inches, the narrower
side b. c. 13. inches, the length 40. inches. Now I must
seek the bzoader side 20 in the upper margine of the table.
The narrower side 13. must be found in the right side and
hanging margine. At their common meeting 16. inches,
and 1/2 part of an inch shall appear.

This true square must be searched for in the table of timber measure. There, found look for 16. in the margine of this table. In the squares with him rightward, see how many 6. inches, and 3/4, which is three quarters of an inch. Some deal with the feet of your Ruler than 6. and 3/4, laid out upon the Timber maketh a foot square. And that measure so directly handled, is contained in the length of your timber six times.

Oberefoze affirme six foot there to be, beside that is left 1/2 part of a foot. Note because the squares at all times (in this Ensample circle not to even inches, but sometime to odd parts : therefoze according to your discretion, add 02 take away some part moze 02 lesse in setting foath the foot square, as above is perfozned.

It were intollerable tediousness, yea impossible to let foath the true quantities of timber measure, to all odd quantities of squares. The discreet handling of these, the witty shall being to a sufficient exactness.

Of

Timber or Stone.

Of Timber or Stone, 3. 5. 10. 20. or
moe sides square, &c.

The viii. Chapter.

When Timber hath divers equall squares in the head, and so through: first, measure all the square sides round about the head 02 end of the Timber. Then take half the number of the whole measure for one breadth.

Then measure from the Center ( which is the middle of the head, oz end of the Timber ) to the middle of the square side, between the two Angles, and take the measure of that distance for the other breadth. Now refort with the measures of these two breadth, (as tofoze ) to the table of squares: taking the bigger number of breadth in the upper margine, and the other lesser in the side margine : with the square there found, have recourse to the table of timber measure, and done as I have instructed.

Ensample.

Admit this small piece of Timber fide
square, e. f. g. h. should be measured, every
side being 12. inches. If ye add together
in one summe all the five sides, they make
60. inches. The half is 30. that serbeth
for one breadth. Then the line e. f. in which
goeth from the Center 02 middle of the
square, to the middle of one side, is 8.
inches. The two numbers 30 and 8 must
be sought ( as before ) in the table of
squares following. At the common mæ-
ting, your square shall appear 15. inches, &
&. This square 15. seek in the table of tim-
ber measure. There ye may see right with
it 7. inches, and 3/4. Now because of this,
the odd quantity of the
square

D 2

Square

13

The Art of measuring

square above 15. inches, lay something leste. Then see how often times that measure (so with discretion handled) is from the one end of your timber to the other; and affirme so many times a foot square there to be, as that measure is found in the length of your Logge.

How round and hollow Timber, Steeples,
Pillers, Globes, &c. are to be measured.

The ix. Chapter.

First gird the Log round about with some line; then divide the line which compasseth that timber in two equal parts : keep the one part four the bigger breadth. After, ye shall divide again that whole length, (the two and twentithy part call away) in threee parts, and take the half of one of them four the other narrower breadth. With the measures of these two breadths, halfe to your table, perfozming all things as afoze is opened.

Enfample.

Suppose this little piece of timber,
i. k. 1. m. were to be measured, the com-
pass of girding 36. inches, and the half
of that is 18. being the one breadth: then
the third 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 perfozmed as befoze) ye shall
find in this round Log, the length 1. m.
being 18. inches, 1. foot, and 1/2 part of a
foot. This is sufficient for all such like.

Timber, Steeples, &c.

A note of hollowed Timber.

If it chance that hollowed Timber be to be measured: measure the whole Logge as though it were not hollow, as above is declared. Then measure the narrower and broader side of the hollow, and see what is contained in that, as though it were matter Timber. Now pull out the content of it, from the whole above measured: the remain of fource must be how much Timber is included in that hollowed body.

I am unable in few words to express to the unlearned, by what mean Pyramidall, or picked regular Steeple of all fashiones are measured. Also how Pillars, how the content of Globes or Bowles are searched, unless the art of numbing were talked. That being known: thus (as now followeth) I teach.

How the cransitode of picked
Steeple is known.

Multiply the plain of the Base in the third part of the height; so you have the cransitode. Or, multiply the content of the superfictall (found as I have infructe) in the height of the Steeple, taking four your purpose the third part of that product.

How the content of Pillers.
is known.

E Create the Base plain in his altitude or height; so have ye your degree.

D. 3

How

["# The Art of measuring", "## How the Cubicall 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 multiply the plain of the Circle in the whole Diameter: then take two third parts, which added, make the Circlesitude.", "### Of the half Circle.", "Is superficial content multiplied (as I said) halvingeth the magnitude of him. If any man require ensamples of these laſt matters, or more sufficient handling; let them refelect unto my books published of Geometry, where they shall be ſatisfied. These little appertain to Carpenters or Pafons: thereſoze not by enſample declared.", "### A generall note.", "VV. When thou Chalt be put to measure some body, without order or fashion, lacking part of his square, or having more than his ſoame: if it lack, thou Chalt 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.", "And when there resulteth any more than the ſoame or regular ſquare: first measure the ſquare Body; then the Circumsode which abouneth. All put together one with the whole irregular Body. This ſufficeth.", "A", "15", "## A Table to finde 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 of Timber: thereſoze 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, ſignifie the inches of the narrower side: and to conclude briefly, the element or figures set in every ſquare room, betoken the juſt square. The bigger figures leftward in every ſquare place, ſignifie the whole inches. And the other lesser rightward in the same ſquare divided by a line, the parts of inches, 1/2 etc.", "This first fraction toward the left hand, betokeneth one half part of an inch: the other two fifts of an inch, and every figure or fraction having a point adjoyned unto him, some deal less than that part is: as that part 1/2, representeth 1/2 a repreſenteth 1/4 a quarter, 1/8 a eighths, 1/16 a twelfths, 1/32 a thirteths, 1/64 a sixteenth, 1/128 a八之一, 1/256 a八之一八, 1/512 a八之一二, 1/1024 a八之一三, 1/2048 a八之一四, 1/4096 a八之一五, 1/8192 a八之一六, 1/16384 a八之一七, 1/32768 a八之一八, 1/653600 a八之一九, 1/1310703184 a八之一十, 1/2650376096 a八之一十一, 1/53048136576 a八之一十二, 1/117693427296 a八之一十三, 1/234785713840 a八之一十四, 1/468941562640 a八之一十五, 1/932773277600 a八之一十六, 1/18791360732800 a八之一十七, 1/37382881408000 a八之一十八, 1/64177125680000 a八之一十九, 1/128693138208000 a八之二, 1/322385695616000 a八之二二, 1/1024000000000000 a八之二三, 1/2048000000000000 a八之二四, 1/4096000000000000 a八之二五, 1/819200000000000 a八之二六, 1/1638400000000000 a八之二七, 1/3276800000000000 a八之二八, 1/6536000000000000 a八之二九, 1/1310703184000000 a八之三十, 1/2650376096000000 a八之三一, 1/530481365760000 a八之三二, 1/1176934272960000 a八之三三, 1/234785713840000 a八之三四, 1/468941562640000 a八之三五, 1/93277327760000 a八之三六, 1/187913607328000 a八之三七, 1/37382881408000 a八之三八, 1/653600000000000 a八之三九, 1/1310703184000000 a八之四, 1/2650376096000000 a八之四一, 1/530481365760000 a八之四二, 1/1176934272960000 a八之四三, 1/234785713840000 a八之四四, 1/468941562640000 a八之四五, 1/93277327760000 a八之四六, 1/187913607328000 a八之四七, 1/37382881408000 a八之四八, 1/653600000000000 a八之四九, 1/1310703184000000 a八之五, 1/2650376096000000 a八之五一, 1/530481365760000 a八之五二, 1/1176934272960000 a八之五三, 1/234785713840000 a八之五四, 1/468941562640000 a八之五五, 1/93277327760000 a八之五六, 1/187913607328000 a八之五七, 1/37382881408000 a八之五八, 1/653600000000000 a八之五九, 1/1310703184000000 a八之六, 1/2650376096000000 a八之六一, 1/530481365760000 a八之六二, 1/1176934272960000 a八之六三, 1/234785713840000 a八之六四, 1/468941562640000 a八之六五, 1/93277327760000 a八之六六, 1/187913607328000 a八之六七, 1/37382881408000 a八之六八, 1/653600000000000 a八之六九, 1/1310703184000000 a八之七, 1/2650376096000000 a八之七一, 1/530481365760000 a八之七二, 1/1176934272960000 a八之七三, 1/234785713840000 a八之七四, 1/468941562640000 a八之七五, 1/93277327760000 a八之七六, 1/187913607328000 a八之七七, 1/37382881408000 a八之七八, 1/653600000000000 a八之七九, 1/1310703184000000 a八之八, 1/2650376096000000 a八之八一, 1/530481365760000 a八之八二, 1/1176934272960000 a八之八三, 1/234785713840000 a八之八四, 1/468941562640000 a八之八五, 1/93277327760000 a八之八六, 1/187913607328000 a八之八七, 1/37382881408000 a八之八八, 1/653600000000000 a八之八九, 1/1310703184000000 a八之九, 1/2650376096000000 a八之九一, 1/530481365760000 a八之九二, 1/1176934272960000 a八之九三, 1/234785713840000 a八之九四, 1/468941562640000 a八之九五, 1/93277327760000 a八之九六, 1/187913607328000 a八之九七, 1/37382881408000 a八之九八, 1/653600000000000 a八之九九, 1/1310703184000000 a八之十, 1/2650376096000000 a八之十一, 1/530481365760000 a八之十二, 1/1176934272960000 a八之十三, 1/234785713840000 a八之十四, 1/468941562640000 a八之十五, 1/93277327760000 a八之十六, 1/187913607328000 a八之十七, 1/37382881408000 a八之十八, 1/653600000000000 a八之十九, 1/1310703184000000 a八之十一, 1/2650376096000000 a八之十一, 1/530481365760000 a八之十一, 1/1176934272960000 a八之十一, 1/234785713840000 a八之十二, 1/468941562640000 a八之十二, 1/93277327760000 a八之十三, 1/187913607328000 a八之十四, 1/37382881408000 a八之十五, 1/653600000000000 a八之十六, 1/1310703184000000 a八之十七, 1/2650376096000000 a八之十八, 1/530481365760000 a八之十八, 1/1176934272960000 a八之十八, 1/234785713840000 a八之十九, 1/468941562640000 a八之二十, 1/93277327760000 a八之二十一, 1/187913607328000 a八之二二, 1/37382881408000 a八之二三, 1/653600000000000 a八之二四, 1/1310703184000000 a八之二五, 1/2650376096000000 a八之二六, 1/530481365760000 a八之二七, 1/1176934272960000 a八之二八, 1/234785713840000 a八之二九, 1/468941562640000 a八之三十, 1/93277327760000 a八之三一, 1/187913607328000 a八之三二, 1/37382881408000 a八之三三, 1/653600000000000 a八之三四, 1/1310703184000000 a八之三四, 1/2650376096000000 a八之三五, 1/530481365760000 a八之三六, 1/1176934272960000 a八之三七, 1/234785713840000 a八之三八, 1/468941562640000 a八之三九, 1/93277327760000 a八之四, 1/187913607328000 a八之四一, 1/37382881408000 a八之四二, 1/653600000000000 a八之四三, 1/1310703184000000 a八之四五, 1/2650376096000000 a八之四六, 1/530481365760000 a八之四七, 1/1176934272960000 a八之四八, 1/234785713840000 a八之四九, 1/468941562640000 a八之五, 1/93277327760000 a八之五一, 1/187913607328000 a八之五二, 1/37382881408000 a八之五三, 1/653600000000000 a八之五四, 1/1310703184000000 a八之五六, 1/2650376096000000 a八之五七, 1/530481365760000 a八之五八, 1/1176934272960000 a八之五九, 1/234785713840000 a八之六, 1/468941562640000 a八之六一, 1/93277327760000 a八之六二, 1/187913607328000 a八之六三, 1/37382881408000 a八之六四, 1/653600000000000 a八之六五, 1/1310703184000000 a八之六六, 1/2650376096000000 a八之六七, 1/530481365760000 a八之六八, 1/1176934272960000 a八之六九, 1/234785713840000 a八之七, 1/468941562640000 a八之七一, 1/93277327760000 a八之七二, 1/187913607328000 a八之七三, 1/37382881408000 a八之七四, 1/653600000000000 a八之七五, 1/1310703184000000 a八之七六, 1/2650376096000000 a八之七七, 1/530481365760000 a八之七八, 1/1176934272960000 a八之七九, 1/234785713840000 a八之八, 1/468941562640000 a八之八一, 1/93277327760000 a八之八二, 1/187913607328000 a八之八三, 1/37382881408000 a八之八四, 1/653600000000000 a八之八五, 1/1310703184000000 a八之八六, 1/2650376096000000 a八之八七, 1/530481365760000 a八之八八, 1/1176934272960000 a八之八九, 1/234785713840000 a八之九, 1/468941562640000 a八之九一, 1/93277327760000 a八之九二, 1/187913607328000 a八之九三, 1/37382881408000 a八之九四, 1/653600000000000 a八之九五, 1/1310703184000000 a八之九六, 1/2650376096000000 a八之九七, 1/530481365760000 a八之九八, 1/1176934272960000 a八之九九, 1/23478571

The Table of Timber measure,
with the declaration and use of it.

The x. Chapter.

The Table (as ye see) is divided into
two Columns of Moins: the one be-
re choct, the other longer. In the head of the
Arct, I have put this wozd Foot: in the se-
cond row Inches, and parts to signifyke set,
Inches and parts of Inches. The Summes
in the margine and left part of the Arct and
Second Columne, declare the quantity of the
square of Timber of Stone from 1. to 36.
Inches Square. Within the rows you may
finde the just length to a foot square, if ye
enter into them in right order according to
the square.

Enlample.

Suppose the Square of your Timber
were 7. inches and that ye desire to
know what measure of length of the ruler
would make a foot square: seek in the left
Margine, seven inches: and with him in
that order toward the right hand, go half
and 2. foot, 11. inches and 3. of an inch.
Note because the fraction 2/3 hath a prick by
him, it betokeneth some small quantity less
than 2/3 of an inch. If it had two pricks of
points thus: 2/3 it should signifyle some little
quantity more. Neither maketh it matter
whether ye observe this pricking of 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 understood of Stones,
likewise to be measured.

Thus is finished their measurng of Timber.
Now ensueth of Board.

16

# The Art of measuring

## Ensample.

Suppose I have a piece of glass, 02 a Board, whose breadth is 22. inches, 4. the length 16. foot. In the fourth magnitude, I find this breadth, 22. 2/3. And even with it in the table rightward, I see 6. inches, 2/3. So much of my Ruler wanting some small quantity, maketh a foot.

How because in the length of my board (which is 16. foot) that measure is found 29. times, and 2/3. parts, I conclude 29. foot there to be, and two third parts of a foot Square, amounting to the length and breadth I said (wanting some small quantity) because of the point joined to this fraction, which is put to dimineth the fraction some little thing, as is declared plainly in the other Tables before put forth.

He that desireth to measure Chamberfloozes Pavedments, or such like, let him only multiply the breadth with the length, so the product heeth the content.

## Example.

If there were a pavement 100. foot long, and in breadth 50. A must needs conclude by multiplication of the length in the breadth there to be contained 5000. foot.

Or thus without Arithmetick; 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 of wages it serves your turn. Of this matter to put forth Tables were superfluous tediousnes and folly. The ingenious with these few will be satisfied.

The

## The Carpenters Ruler.

The face of the Carpenters 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 to common among good Artificers, I will not spend my words in opening it. Behold the figures and learn by them how they ought to make and commonly to deck your Ruler both with timber & board measure.

### Ensample.

Admit the Ruler be as a. b. c. d. well plained 12. inches 20 long, a quarter of an inch thick, and two inches in breadth. 19 Truly it were more convenient, if it had two foot in length. 18 This Ruler here imagined, but a foot in length is divided first in 12. even parts called inches: then every inch in half 02 two equal portions; each half in two quarters; every quarter in four 02 two parts at the least; 15 as in this Ensample. Then are the figures placed from 1. to 12. manifesting the inches. 14 Thus your Ruler is ready to receive the measures which are 13 marked 02 figured on your Ruler thus. Add first the timber measure, as followeth.

Timber measure.

The Carpenters Ruler.

The common use of the Carpenters Ruler,
touching the face afore put forth.

The xiii. Chapter.

eighth
pier show-
new he
square is
id.

Oppose a peece of Timber be moaten, whole
true square is 7. inches, this square appointed
you to the figure of 7. in the line g. h. under
whom rightward in the place alligned to Tim-
ber measure is written 2. foot, 11. inches, 7/2.
As often as that measure is found in the length
of your Timber, so many foot of Timber is in that peece.

Another Enlample,

Imagine your square to be 22. inches : seek in the line x. 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. There-
foze lay out the 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.
Hast the breadth upon your Ruler, in the room 22 place of
board measure, and immediately before your eyes they remain-
eth what is to be laid out to make a juck foot of board.

The use of the principall lines in the Geome-
tricall Quadrant on the backside of the Ruler,
and first of the levell line.

The xv. Chapter.

I behooveth you to look through your lights
q. n. placed in the thickness of lines k. m. a fine
thread and plummet falling at liberty out of the
center n. If this plummet and thread chance pre-
cisely on the line of levell (which is n. o. whatso-
ver ye see through the lights, is levell with your eye, if other
wise

The use of the Scale.

wise the thing that ye look unto is not levell, either more or
lesse then the height, or levell of your eye: More, if the plum-
met fall to you ward: less, if contrary.

How by the Line of Levell to foresee whether
the water of any Spring or head is possible to be
brought to a place appointed, and also to judge
the wholedomns of it.

The xvi. Chapter.

Thall goe to the head or Sping, and set your Ru-
ler to your eye (being in height equall with the
water) so that the fine cord and plummet fall pre-
cisely in the line of levell. Now if through the
lights ye may see above the place, know and judge
the water possible to be through : if your sight fall under, im-
possible. It commeth commonly to pales, when the place to
which ye would have water conveyed, is of any great diffrence
from the head, then Hills, Valleyes, and such like impedis-
ments, let the line befall to have his free course : wherefore
this remedy is provided. At the head of the Sping, ye shall
look through the lights (as before) and note a mark, in the next
Hill toward the place, then goe to the mark, in like manner
observe another in some Hill : so forth untill by any of them
ye may perceive the place desired. If then your sight running,
through the pins of your Ruler (the thread ever falling on the
Line n. o. ) erred that place, the conveying of your water is
possible : otherwise not.

Now by the way hizely ye shall be instructed, how ye may
know the wholedomns.

How good water is known.

Take a clean Pot, and put water in it: so let it on the fire :
after a little boiling, powre it out, if then no filth re-
main.

20

## The use of the Scale.

mat in the bottom of the pot, it may be judged the wholcomer. D2 thus. Let fall drops upon metall, oz rather on glas (any of them being pollished) and suffer that to dry by it self: if after there remain no spot oz signe, it is a good token. Moze, over, if your water be sweet, pure, clear, light, oz of little weight, it followeth the water to be wholesome for the use of man.

## Of the Line of Height.

When ever the Thread and Plummet doe chance jut, ly on the Height, 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, equall with your standing, adding the height 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

It is age also any thing plumbe upright when the thickness of your Ruler i. 1. is closely thereon, the Plummet then at little falling on q. n. named the line of heights upward. Now followeth the rule of the Scale.

### To search out Heights by the Scale
with the aid of two places.

The viii. Chapter.

Et the Thread and Plummet fall in the one, on the 12. points : in the other station on the 6. of the right shadow : double the distance between the two places, the summitie appeareth from that part of the thing measured, which is equall

## The use of the Scale.

21

in height with your eye. D2 the one in the 12. the other in 8. of right shadow: then triple the distance. The one in 12. the other in 6. of right quadruple the space. The one in 12. the other in 6. of the contrary shadow, then the space between both the stations is equall with that ye measure, ever understanding from your eye upward. Even that same cometh to palls, if in the one the Thread be found upon the 6. of the contrary, in the other on the 4. of the same, or the 4. and 3. of the contrary. In all these the spaces are equall 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 appearing : the Base being equall with your standing.

I would not have you ignorant here how to know lengths which be in the height not easily to come unto. Foz (as before) get the height of the top, the altitude of the Base or longer part of your length. Subtract the least height out of the moze, of force your desired length remaineth. D2 thus : Let the plummet and thread fall in the 12. Mark your place : goe 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 lengths in heights are known.

### How with Scale direct or upright, heights by their shadowes are declared.

The ix. Chapter.

Arn your left side unto the Sun, suffering his beams to pearce both your lights q. r. placed (as above is said) in the thickness of line k. m. The thread or plummet then hanging at liberty, out of the Centers, theweth as well the degrees of height to be counted from o. as the parts

f 2

The use of the

The parts of the Scale cut. If your thread be found in the 12. part of 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 lights, which I name points of the right shadow, then 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 fifth, twice: and 1/2. of the shadow; in the first twice; in the seventh once, and 1/2. in the eighth once, and 1/4. in the ninth once, and 1/4. in the tenth once, and 1/8. in the eleventh ye shall take the shadow once, and 1/16. 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.

Contrary shadow.

But if it be in the parts of the contrary shadow, augment the length of the shadow with the parts declared by the plummet: and in the increase divide them by 12, so cometh the altitude also.

Thus the composition and whole appliance of the Carpenters' Ruler is shown: 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 expresseth, wherefore I leave to write in that behalf. Notwithstanding I will declare how heights and lengths are taken, etc. matters rare and known of few Artificers.

Also be tables to get a true knowledge of the day, hour, and that divers waves, with the help of the Squire, as is opened in my general Pzognostication, augmented in the year of our LORD 1556.

What

Carpenters Squire.

What length the fides of the Squire ought to be, and the division of him.

The xx. Chapter.

I Aced not to put forth the exact making of this Instrument so well known. Lo therefoze the figure. One side supplied 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. into b. into 12. equall principall parts, and every of them into a less (if ye lift) each containing 10. minutes, also the side c. d. in the outward contrary, plain from the top c. into d. is divided into 12.

even portions; and again (if ye require exactness) every of them in 6. each of value 10. minutes. Behold a line and plummet falling from c. to f. a parallel to c. d. and a. b. Thus this Squire is well framed for the use of divers Tables put forth in my general Pzognostication, and also for the finding of altitudes and longitudes, which here I purpose now briefly to open.

How by the Squire heights are known.

A Altitudes or heights are found, the line or plummet contained in the first point, cutting h. the middle of a. g. The moveable.

F 3

## The use of the

movable lights placed in a. g. oz a parallax from that line not unlike, as is opened of the line of height, in the back of my Ruler.

How lengths in plain ground are searched by the Carpenters or Masons Squire.

The xxi. Chapter.

Aske a Staffe divided into certain portions as ye lift, in a 100. oz a 1000. parts. At the beginning of your length, upon the very top directly standing, let in the inward Angle of the Squire : lift up oz put down this instrument untill you see the furthest part of your length, I mean untill your sight running from that Angle, to the end of your Squire, come unto the furthest part of that length. The Squire so remaining, and the Staffe not removed from his height. Marke where the other end of the Squire nert unto you noted upon the ground. See what proportion the Staffe then beareth to the part of the ground, which the nereest end of the Squire pointed unto from the Staffe: the same shall the length have to the quantity of the same Staffe.

### Enlample

The Staff a. c. in this figure is imagined 6. ftot, and the space a. d. 2. ftot. Considering now that 6. the length of the Staffe containeth 2. threes, therefize the longitude desired, a. d. of force must contain three times the Staffe (which Staffe is 6. ftot) that maketh 18. ftot. As this is proved true by small ground in the figure following : so the art faileth not in a greater space, which the good Speculator and gent

The cause is taken out of Euclid. 33 pro. 1 Book and the 4. pro. 6. Book.

## Carpenters Squire.

gent Practiser by any way cannot deny. Yet experience willeth me this to confess, that the Squire is not convenient for any long distance, but the instrument geometricall ( whole making and use ye may perceive in the treatise following ) unless ye ascend some tree oz current for your aid, which length known, shall stand in stead of your Staffe.

### A Note.

It behoeth you to have a fine cord, made fast in the upper part of your Staffe, 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 Squire from the Staffe pointed, as ye see d. c. the other end then truly directing to the furthest distance.

Know that the ground must be very plain and level, otherwise error must ensue.

Thus the use of the Squire is here somewhat declared, but more in my general Prognostication, peea most plentifully hereafter (God sparing life) in a book titled, The rate use of the Squire in practises. Mathematicall. In the which book profitable plesant experiences shall be plainly opened (omely of me practised) as well of perspective, as of the Mathematicalls in generall.

A

## The use of the

as occasion shall be given: which all are easily to be perceived by the figure following, although we rude declaration hath not expressed my meaning.

Here note in the lead of your short:aves, ye may have one Croft:staffe two foot long, with currant lights, so artificially made, that always the short staffe shall rung (quire upon the longer, and the lights distinct, as ye lift to place them.

Things needfull to be known before the use of this Instrument is opened.

### The vii. Chapter.

Ecoze I intreat of this use, it behoveth to know things necessary, and best, which of the five little staffes g.h.i.k.l. mentioned in the maing, is to be put on your long staffe e.f. according to the distance of the mark. Note if your mark be near hand, be it length, breadth, or height, the longer g. doth seem most fit to have the room, if more of length, the other h. and to the further distance, the shorter the staffe requireth to be, which shall occupe that place. Ort practise howeith this better than many words. Also note, if chance be to goe in toward your mark, (as after you shall see how) you must remove the short staffe inward inore near to the end of the longer e. If you be compelled to goe from it, then put it from e. toward the end f. Also remember when you are appointed to measure any breadth or length (as shall be declared) it behoveth you to stand right with, and against that breadth: yes, and the longer the breadth or larger the width, or length is, the better the thing will come to palls. And for heights it is necessary, if you regard all preciseness to have the height, stand directly up.

Note this that followeth to be generally in all workings

Ye must stand right up with your Body and Deck, your feet just together, your hands not much moving, the one eye

## profitable Staffe.

eye closed, and ever mark your standing right with the midmost of your feet. We not ignozant here, that I call the streams of the little staffes, the very ends where the light ever runneth. And no difference between the Altitude and height, between the longitude and length: the latitude and breadth. The short staffe I name the letter figured over them. Your eye must ever be placed in the end of the longer staffe e. and with the other eye ye ought to wink.

These trifles and such like omitted, lettheth the truth to come to palls, and make men to suspect the ground, which is most certain.

What these words mean, Longitude, Latitude, Altitude.

How heights standing directly up, are measured by the Instrument.

### The iii. Chapter.

At the staffe g. upon the longer e. f. and move him his just length from the beginning of the longer e. turn the ends of g. toward you, and according to that height placing your eye (as is said) ever at the beginning of the longer e. with the other eye wink. Then goe back until ye may plainly perceive the very upper part of that altitude; and also the lower end by the extremes of your shorter staffe g. Now the space of the middle of your foot to the base of the height is equal with the altitude.

### Or thus.

When ye shall see any altitude, whose measure ye require, imagine by conjecture how oftentimes that height is found in the space from it unto your standing. Then move your shorter staffe (choosing as above most convenient) even as often his own length from the beginning of the longer e.

C 2

where

## The use of the

Where your eye is ever placed. This done, turn the ends of your little Staffe, your eye being in e. according to the height: look whether ye may see by the extremes of your Chozter the very top, and also the lowest part of the height. If not, move the Chozter a length further toward e. or more to e. as ye see cause, and as your confection failed. Or let your little Staffe remain, as by confection he was put, and goe toward e. from that height, until the altitude agree sufficiently with the extremes of your Chozt Staffe. Then mark that place with the midrest of your foot.

Now ye may conclude, that the height is as often contained in the distance, which is between the mark and it, as the length of that little Staffe is found removed from the end of the longer, etc.

### Ensample.

If the Chozt Staffe be ten times his own length from e. affirm the height contained in that distance ten times only.

How he just height is known.

The altitude is thus gotten. Move your Chozt Staffe from his late being a length either toward e. from e. as ye lift to goe in e. back. Then goe from e. nor unto it (as before) until the very summit, and also the lowest part of the height agree with the extremes of your Chozter Staffe. The space then between your marked place and this latter, declareth the just height. At first times through impediments, ye shall not have room to goe so farre back as forward, as the height commeth unto. This remedy is provided. Move the little Staffe half his length, and so seek two stations (as before) until the extreme of the Chozter Staffe be found sufficiently farre either end of the height. Then the space between the two stations must be doubled to have the just height: or if you lift, ye may move the Chozter, according to the fourth part of his length, or to any portion, as to the fift, sixt, twenty, etc. then shall ye see that part of the height between the two stations.

A remedy provided for want of ground.

Yet

## profitable Staffe.

Yet know this (which experience by diligent practice will shew) the bigger parts ye take, the less roz ye commit. A little roz often multiplied, increases to a great.

Now that all the above spoken may the better be perceived, behold the example ensuing, as ye may see by figure declared, in the which the height is imagined a. b. the first station c. the Chozt Staffe d. is moved from e. just his length. I am forced to conclude, that the base of the height a. b. is from my standing e. even his precise length. So then if you measure that distance of a. c. being 13. paces, ye have the true height of a. b. as many as in the other standing place d. the Chozter Staffe is found from e. twice his length and a half, wherefore I must affirm the height a. b. to be contained in 2 found in the distance a. d. twice and a half: which length a. d. is apparent 32 paces. All this that is spoken of the height may well be understood of latitudes or widths and lengths following.

The ground of this may be gathered of two: in his perspective, 1. Theo.

In altitudes this rule is not perfect, except the eye be level with the middle of the altitude.

3

26

How.

The use of the

How the breadth or wideness of things
are found, and by them, length or any
distance at pleasure.

The viii. Chapter.

W
atsoever I have instructed afore of heights, the
same understand here of wideness, lengths, &c.
For none otherwise are latitudes or widenesses
searched by this Instrument, then before is de-
clared of heights, only this excepted, that the
horst Kaffe must lie contrary, the ends accor-
ding to the breadth, seeing by the extremes of the horst Kaffe,
the new uttermost parts or ends of the latitude, noting your
stations right with the midst of your foot; and so perfozr all
as tofoze. And as I said, thereof the parts of the height found
between your findings, even the same things is well used
here, for all manner parts of the breadth.

Enfample.

The breadth in this figure following supposed a. b. Also the first station c. the next d. My desire is to know the widthesse a. b. and the length of distance d. b. Marke how the ends of the letter Kanes are turned to the extremes of the widthesse. When behold how the horst Kaffe in c. is but once his length removed from e. Wherefore (by the instructions of heights a. kore) I may boldlie say, that the widenesss a. b. is but once contained between d. and b. and that measure is found 12. scoze, as much as is the other a. b. In the second standing d. the little Kaffe is removed thix times his length from e. For that cause I conclude (and truly) from b. to that station thix times the breadth, which breadth is 12. scoze. So by the widenesss I have found the length of b. d. 36. scoze, my desire. Thus are latitudes found, and by them lengths, &c.

Behold

profitable Staffe.

Behold the Figure.

Yee must alwaies stand directly against the
middle of the breadth

Whensoever any distance is put, whole certain length we require: measure (by the art expressed) either the height of any thing there found, or the breadth, and see how oftentimes that wideness or length is contained unto your standing; which known, the length cannot be hid, as is declared.

Now in few words to conclude, ye may by this Instrument measure the distance of Houses, Stables, Trees, the length of Walles, and breadth of Ditches, Images in height, and such like. The good wittie Carpenter standing in a place, where he may plainly see a whole House, or any manner of frame with great pleasure, may by this get a pædily the true proportion of that House, which he ought to note in a table, and when time cometh (not without his great praise) may make, reare, and set up the like. This I take to be sufficient for these Craftsmen.

A more large
use of this In-
strument.

I have