the perfect Analogicall description of the Ocean Sea coastes, through
the whole world: or in the chiefe and principall partes thereof:” with
the Iles and chiefe particular places of daungers, conteyned within the
boundes, and Sea coastes described: as, of Quicksandes, Bankes, Pittes,
Rockes, Races, Countertides, Whorlepooles. &c. This, dealeth with the
Element of the water chiefly: as _Geographie_ did principally take the
Element of the Earthes description (with his appertenances) to taske.
And besides thys, _Hydrographie_, requireth a particular Register of
certaine Landmarkes (where markes may be had) from the sea, well hable
to be skried, in what point of the Seacumpase they appeare, and what
apparent forme, Situation, and bignes they haue, in respecte of any
daungerous place in the sea, or nere vnto it, assigned: And in all
Coastes, what Mone, maketh full Sea: and what way, the Tides and Ebbes,
come and go, the _Hydrographer_ ought to recorde. The Soundinges
likewise: and the Chanels wayes: their number, and depthes ordinarily,
at ebbe and flud, ought the _Hydrographer_, by obseruation and diligence
of _Measuring_, to haue certainly knowen. And many other pointes, are
belonging to perfecte _Hydrographie_, and for to make a _Rutter_, by: of
which, I nede not here speake: as of the describing, in any place, vpon
Globe or Plaine, the 32. pointes of the Compase, truely: (wherof,
scarsly foure, in England, haue right knowledge: bycause, the lines
therof, are no straight lines, nor Circles.) Of making due proiection of
a Sphere in plaine. Of the Variacion of the Compas, from true Northe:
And such like matters (of great importance, all) I leaue to speake of,
in this place: bycause, I may seame (al ready) to haue enlarged the
boundes, and duety of an Hydographer, much more, then any man (to this
day) hath noted, or prescribed. Yet am I well hable to proue, all these
thinges, to appertaine, and also to be proper to the Hydrographer. The
chief vse and ende of this Art, is the Art of Nauigation: but it hath
other diuerse vses: euen by them to be enioyed, that neuer lacke sight
of land.
+‡Stratarithmetrie‡+, is the Skill, (appertainyng to the warre,) by
which a man can set in figure, analogicall to any _Geometricall_ figure
appointed, any certaine number or summe of men: of such a figure
capable: (by reason of the vsuall spaces betwene Souldiers allowed: and
for that, of men, can be made no Fractions. Yet, neuertheles, he can
order the giuen summe of men, for the greatest such figure, that of
them, cã be ordred) and certifie, of the ouerplus: (if any be) and of
the next certaine summe, which, with the ouerplus, will admit a figure
exactly proportionall to the figure assigned. By which Skill, also, of
any army or company of men: (the figure & sides of whose orderly
standing, or array, is knowen) he is able to expresse the iust number of
men, within that figure conteined: or (orderly) able to be conteined.
[* Note.]
* And this figure, and sides therof, he is hable to know: either beyng
by, and at hand: or a farre of. Thus farre, stretcheth the description
and property of _Stratarithmetrie_: sufficient for this tyme and place.
[The difference betwene Stratarithmetrie and Tacticie.]
“It differreth from the Feate _Tacticall_, _De aciebus instruendis._
bycause, there, is necessary the wisedome and foresight, to what purpose
he so ordreth the men: and Skillfull hability, also, for any occasion,
or purpose, to deuise and vse the aptest and most necessary order, array
and figure of his Company and Summe of men.” By figure, I meane: as,
either of a _Perfect Square_, _Triangle_, _Circle_, _Ouale_, _long
square_, (of the Grekes it is called _Eteromekes_) _Rhombe_, _Rhomboïd_,
_Lunular_, _Ryng_, _Serpentine_, and such other Geometricall figures:
Which, in warres, haue ben, and are to be vsed: for commodiousnes,
necessity, and auauntage &c. And no small skill ought he to haue, that
should make true report, or nere the truth, of the numbers and Summes,
of footemen or horsemen, in the Enemyes ordring. A farre of, to make an
estimate, betwene nere termes of More and Lesse, is not a thyng very
rife, among those that gladly would do it.
[I. D.
Frende, you will finde it hard, to performe my description
of this Feate. But by Chorographie, you may helpe your selfe
some what: where the Figures knowne (in Sides and Angles)
are not Regular: And where, Resolution into Triangles can
serue. &c. And yet you will finde it strange to deale thus
generally with Arithmeticall figures: and, that for Battayle
ray. Their contentes, differ so much from like Geometricall
Figures.]
Great pollicy may be vsed of the Capitaines, (at tymes fete, and in
places conuenient) as to vse Figures, which make greatest shew, of so
many as he hath: and vsing the aduauntage of the three kindes of vsuall
spaces: (betwene footemen or horsemen) to take the largest: or when he
would seme to haue few, (beyng many:) contrarywise, in Figure, and
space. The Herald, Purseuant, Sergeant Royall, Capitaine, or who soeuer
is carefull to come nere the truth herein, besides the Iudgement of his
expert eye, his skill of Ordering _Tacticall_, the helpe of his
Geometricall instrument: Ring, or Staffe Astronomicall: (commodiously
framed for cariage and vse) He may wonderfully helpe him selfe, by
perspectiue Glasses. In which, (I trust) our posterity will proue more
skillfull and expert, and to greater purposes, then in these dayes, can
(almost) be credited to be possible.
Thus haue I lightly passed ouer the Artificiall Feates, chiefly
dependyng vpon vulgar _Geometrie_: & commonly and generally reckened
vnder the name of _Geometrie_. But there are other (very many)
_Methodicall Artes_, which, declyning from the purity, simplicitie, and
Immateriality, of our Principall Science of _Magnitudes_: do yet
neuertheles vse the great ayde, direction, and Method of the sayd
principall Science, and haue propre names, and distinct: both from the
Science of _Geometrie_, (from which they are deriued) and one from the
other. As +Perspectiue, Astronomie, Musike, Cosmographie, Astrologie,
Statike, Anthropographie, Trochilike, Helicosophie, Pneumatithmie,
Menadrie, Hypogeiodie, Hydragogie, Horometrie, Zographie, Architecture,
Nauigation, Thaumaturgike+ and +Archemastrie+. I thinke it necessary,
orderly, of these to giue some peculier descriptions: and withall, to
touch some of their commodious vses, and so to make this Preface, to be
a little swete, pleasant Nosegaye for you: to comfort your Spirites,
beyng almost out of courage, and in despayre, (through brutish brute)
Weenyng that _Geometrie_, had but serued for buildyng of an house, or a
curious bridge, or the roufe of Westminster hall, or some witty pretty
deuise, or engyn, appropriate to a Carpenter, or a Ioyner &c. That the
thing is farre otherwise, then the world, (commonly) to this day, hath
demed, by worde and worke, good profe wilbe made.
Among these Artes, by good reason, +‡Perspectiue‡+ ought to be had, ere
of _Astronomicall Apparences_, perfect knowledge can be atteyned. And
bycause of the prerogatiue of _Light_, beyng the first of _Gods
Creatures_: and the eye, the light of our body, and his Sense most
mighty, and his organ most Artificiall and _Geometricall_: At
_Perspectiue_, we will begyn therfore. +Perspectiue, is an Art
Mathematicall, which demonstrateth the maner, and properties, of all
Radiations Direct, Broken, and Reflected.+ This Description, or
Notation, is brief: but it reacheth so farre, as the world is wyde. It
concerneth all Creatures, all Actions, and passions, by Emanation of
beames perfourmed. Beames, or naturall lines, (here) I meane, not of
light onely, or of colour (though they, to eye, giue shew, witnes, and
profe, wherby to ground the Arte vpon) but also of other _Formes_, both
_Substantiall_, and _Accidentall_, the certaine and determined actiue
Radiall emanations. By this Art (omitting to speake of the highest
pointes) we may vse our eyes, and the light, with greater pleasure: and
perfecter Iudgement: both of things, in light seen, & of other: which by
like order of Lightes Radiations, worke and produce their effectes. We
may be ashamed to be ignorant of the cause, why so sundry wayes our eye
is deceiued, and abused: as, while the eye weeneth a roũd Globe or
Sphere (beyng farre of) to be a flat and plaine Circle, and so likewise
iudgeth a plaine Square, to be roũd: supposeth walles parallels, to
approche, a farre of: rofe and floure parallels, the one to bend
downward, the other to rise vpward, at a little distance from you.
Againe, of thinges being in like swiftnes of mouing, to thinke the
nerer, to moue faster: and the farder, much slower. Nay, of two thinges,
wherof the one (incomparably) doth moue swifter then the other, to deme
the slower to moue very swift, & the other to stand: what an error is
this, of our eye? Of the Raynbow, both of his Colours, of the order of
the colours, of the bignes of it, the place and heith of it, (&c) to
know the causes demonstratiue, is it not pleasant, is it not necessary?
of two or three Sonnes appearing: of Blasing Sterres: and such like
thinges: by naturall causes, brought to passe, (and yet neuertheles, of
farder matter, Significatiue) is it not commodious for man to know the
very true cause, & occasion Naturall? Yea, rather, is it not, greatly,
against the Souerainty of Mans nature, to be so ouershot and abused,
with thinges (at hand) before his eyes? as with a Pecockes tayle, and a
Doues necke: or a whole ore, in water, holden, to seme broken. Thynges,
farre of, to seeme nere: and nere, to seme farre of. Small thinges, to
seme great: and great, to seme small. One man, to seme an Army. Or a man
to be curstly affrayed of his owne shaddow. Yea, so much, to feare,
that, if you, being (alone) nere a certaine glasse, and proffer, with
dagger or sword, to foyne at the glasse, you shall suddenly be moued to
giue backe (in maner) by reason of an Image,
[☞ A marueilous Glasse.]
appearing in the ayre, betwene you & the glasse, with like hand, sword
or dagger, & with like quicknes, foyning at your very eye, likewise as
you do at the Glasse. Straunge, this is, to heare of: but more
meruailous to behold, then these my wordes can signifie. And
neuerthelesse by demonstration Opticall, the order and cause therof, is
certified: euen so, as the effect is consequent. Yea, thus much more,
dare I take vpon me, toward the satisfying of the noble courrage, that
longeth ardently for the wisedome of Causes Naturall: as to let him
vnderstand, that, in London, he may with his owne eyes, haue profe of
that, which I haue sayd herein. A Gentleman, (which, for his good
seruice, done to his Countrey, is famous and honorable:
[S. W. P.]
and for skill in the Mathematicall Sciences, and Languages, is the Od
man of this land. &c.) euen he, is hable: and (I am sure) will, very
willingly, let the Glasse, and profe be sene: and so I (here) request
him: for the encrease of wisedome, in the honorable: and for the
stopping of the mouthes malicious: and repressing the arrogancy of the
ignorant. Ye may easily gesse, what I meane. This Art of _Perspectiue_,
is of that excellency, and may be led, to the certifying, and executing
of such thinges, as no man would easily beleue: without Actuall profe
perceiued. I speake nothing of _Naturall Philosophie_, which, without
_Perspectiue_, can not be fully vnderstanded, nor perfectly atteined
vnto. Nor, of _Astronomie_: which, without _Perspectiue_, can not well
be grounded: Nor _Astrologie_, naturally Verified, and auouched. That
part hereof, which dealeth with Glasses (which name, Glasse, is a
generall name, in this Arte, for any thing, from which, a Beame
reboundeth) is called _Catoptrike_: and hath so many vses, both
merueilous, and proffitable: that, both, it would hold me to long, to
note therin the principall conclusions, all ready knowne: And also
(perchaunce) some thinges, might lacke due credite with you: And I,
therby, to leese my labor: and you, to slip into light Iudgement,
[* ☞]
Before you haue learned sufficiently the powre of Nature and Arte.
Now, to procede: +‡Astronomie‡, is an Arte Mathematicall, which
demonstrateth the distance, magnitudes, and all naturall motions,
apparences, and passions propre to the Planets and fixed Sterres: for
any time past, present and to come: in respect of a certaine Horizon, or
without respect of any Horizon.+ By this Arte we are certified of the
distance of the Starry Skye, and of eche _Planete_ from the Centre of
the Earth: and of the greatnes of any Fixed starre sene, or _Planete_,
in respect of the Earthes greatnes. As, we are sure (by this Arte) that
the Solidity, Massines and Body of the _Sonne_, conteineth the quantitie
of the whole Earth and Sea, a hundred thre score and two times, lesse by
⅛ one eight parte of the earth. But the Body of the whole earthly globe
and Sea, is bigger then the body of the Mone, three and forty times
lesse by ⅛ of the Mone. Wherfore the _Sonne_ is bigger then the _Mone_,
7000 times, lesse, by 59 39/64 that is, precisely 6940 25/64 bigger then
the _Mone_. And yet the vnskillfull man, would iudge them a like bigge.
Wherfore, of Necessity, the one is much farder from vs, then the other.
The _Sonne_, when he is fardest from the earth (which, now, in our age,
is, when he is in the 8. degree, of Cancer) is, 1179 Semidiameters of
the Earth, distante. And the _Mone_ when she is fardest from the earth,
is 68 Semidiameters of the earth and ⅓ The nerest, that the _Mone_
commeth to the earth, is Semidiameters 52¼ The distance of the Starry
Skye is, frõ vs, in Semidiameters of the earth 20081½ Twenty thousand
fourescore, one, and almost a halfe. Subtract from this, the _Mones_
nerest distance, from the Earth: and therof remaineth Semidiameters of
the earth 20029¼ Twenty thousand nine and twenty and a quarter.
[Note.]
So thicke is the heauenly Palace, that the _Planetes_ haue all their
exercise in, and most meruailously perfourme the Commaũdement and Charge
to them giuen by the omnipotent Maiestie of the king of kings. This is
that, which in _Genesis_ is called _Ha Rakia_. Consider it well. The
Semidiameter of the earth, cõteineth of our common miles 3436 4/11 three
thousand, foure hundred thirty six and foure eleuenth partes of one
myle: Such as the whole earth and Sea, round about, is 21600. One and
twenty thousand six hundred of our myles. Allowyng for euery degree of
the greatest circle, thre score myles. Now if you way well with your
selfe but this litle parcell of frute _Astronomicall_, as concerning the
bignesse, Distances of _Sonne_, _Mone_, _Sterry Sky_, and the huge
massines of _Ha Rakia_, will you not finde your Consciences moued, with
the kingly Prophet, to sing the confession of Gods Glory, and say, +_The
Heauens declare the glory of God, and the Firmament =[Ha Rakia]= sheweth
forth the workes of his handes_+. And so forth, for those fiue first
staues, of that kingly Psalme. Well, well, It is time for some to lay
hold on wisedome, and to Iudge truly of thinges: and notso to expound
the Holy word, all by Allegories: as to Neglect the wisedome, powre and
Goodnes of God, in, and by his Creatures, and Creation to be seen and
learned. By parables and Analogies of whose natures and properties, the
course of the Holy Scripture, also, declareth to vs very many Mysteries.
The whole Frame of Gods Creatures, (which is the whole world,) is to vs,
a bright glasse: from which, by reflexion, reboundeth to our knowledge
and perceiuerance, Beames, and Radiations: representing the Image of his
Infinite goodnes, Omnipotẽcy, and wisedome. And we therby, are taught
and persuaded to Glorifie our Creator, as God: and be thankefull
therfore. Could the Heathenistes finde these vses, of these most pure,
beawtifull, and Mighty Corporall Creatures: and shall we, after that the
true _Sonne_ of rightwisenesse is risen aboue the _Horizon_, of our
temporall _Hemisphærie_, and hath so abundantly streamed into our
hartes, the direct beames of his goodnes, mercy, and grace: Whose heat
All Creatures feele: Spirituall and Corporall: Visible and Inuisible.
Shall we (I say) looke vpon the _Heauen_, _Sterres_, and _Planets_, as
an Oxe and an Asse doth: no furder carefull or inquisitiue, what they
are: why were they Created, How do they execute that they were Created
for? Seing, All Creatures, were for our sake created: and both we, and
they, Created, chiefly to glorifie the Almighty Creator: and that, by
all meanes, to vs possible. _Nolite ignorare_ (saith _Plato in
Epinomis_) _Astronomiam, Sapientissimũ quiddam esse._ +_Be ye not
ignorant, Astronomie to be a thyng of excellent wisedome._+
_Astronomie_, was to vs, from the beginning commended, and in maner
commaunded by God him selfe. In asmuch as he made the _Sonne_, _Mone_,
and _Sterres_, to be to vs, for _Signes_, and knowledge of Seasons, and
for Distinctions of Dayes, and yeares. Many wordes nede not. But I wish,
euery man should way this word, _Signes_. And besides that, conferre it
also with the tenth Chapter of _Hieremie_. And though Some thinke, that
there, they haue found a rod: Yet Modest Reason, will be indifferent
Iudge, who ought to be beaten therwith, in respect of our purpose.
Leauing that: I pray you vnderstand this: that without great diligence
of Obseruation, examination and Calculation, their periods and courses
(wherby _Distinction_ of Seasons, yeares, and New Mones might precisely
be knowne) could not exactely be certified. Which thing to performe, is
that _Art_, which we here haue Defined to be _Astronomie_. Wherby, we
may haue the distinct Course of Times, dayes, yeares, and Ages: aswell
for Consideratiõ of Sacred Prophesies, accomplished in due time,
foretold: as for high Mysticall Solemnities holding: And for all other
humaine affaires, Conditions, and couenantes, vpon certaine time,
betwene man and man: with many other great vses: Wherin, (verely), would
be great incertainty, Confusion, vntruth, and brutish Barbarousnes:
without the wonderfull diligence and skill of this Arte: continually
learning, and determining Times, and periodes of Time, by the Record of
the heauenly booke, wherin all times are written: and to be read with an
_Astronomicall staffe_, in stede of a festue.
+‡Musike‡+, of Motion, hath his Originall cause: Therfore, after the
motions most swift, and most Slow, which are in the Firmament, of Nature
performed: and vnder the _Astronomers Consideration_: now I will Speake
of an other kinde of _Motion_, producing sound, audible, and of Man
numerable. _Musike_ I call here that _Science_, which of the Grekes is
called _Harmonice_. Not medling with the Controuersie betwene the
auncient _Harmonistes_, and _Canonistes_. +Musike is a Mathematicall
Science, which teacheth, by sense and reason, perfectly to iudge, and
order the diuersities of soundes, hye and low.+ _Astronomie_ and
_Musike_ are Sisters, saith _Plato_. As, for _Astronomie_, the eyes: So,
for _Harmonious Motion_, the eares were made. But as _Astronomie_ hath a
more diuine Contemplation, and cõmodity, then mortall eye can perceiue:
So, is _Musike_ to be considered,
[1.]
that the * Minde may be preferred, before the eare. And from audible
sound, we ought to ascende, to the examination: which numbers are
_Harmonious_, and which not. And why, either, the one are: or the other
are not. I could at large,
[2.]
in the heauenly * motions and distances, describe a meruailous Harmonie,
of _Pythagoras_ Harpe
[3.]
with eight stringes. Also, somwhat might be sayd of _Mercurius_ * two
Harpes,
[4.]
eche of foure Stringes Elementall. And very straunge matter, might be
alledged of the _Harmonie_,
[5.]
to our * Spirituall part appropriate. As in _Ptolomaus_ third boke, in
the fourth and sixth Chapters may appeare. *
[6.]
And what is the cause of the apt bonde, and frendly felowship, of the
Intellectuall and Mentall part of vs, with our grosse & corruptible
body: but a certaine Meane, and _Harmonious Spiritualitie, with both
participatyng, & of both (in a maner) resultynge In
[7.]
the * Tune of Mans voyce, and also
[8.]
* the sound of Instrument_, what might be sayd, of _Harmonie_: No common
Musicien would lightly beleue.
[I. D.
Read in Aristotle his 8. booke of Politikes: the 5, 6, and 7.
chapters. Where you shall haue some occasion farder to thinke
of Musike, than commonly is thought.]
But of the sundry Mixture (as I may terme it) and concurse, diuerse
collation, and Application of these _Harmonies_: as of thre, foure,
fiue, or mo: Maruailous haue the effectes ben: and yet may be founde,
and produced the like: with some proportionall consideration for our
time, and being: in respect of the State, of the thinges then: in which,
and by which, the wondrous effectes were wrought. _Democritus_ and
_Theophrastus_ affirmed, that, by _Musike_, griefes and diseases of the
Minde, and body might be cured, or inferred. And we finde in Recorde,
that _Terpander_, _Arion_, _Ismenias_, _Orpheus_, _Amphion_, _Dauid_,
_Pythagoras_, _Empedocles_, _Asclepiades_ and _Timotheus_, by
_Harmonicall_ Consonãcy, haue done, and brought to pas, thinges, more
then meruailous, to here of. Of them then, making no farder discourse,
in this place: Sure I am, that Common _Musike_, commonly vsed, is found
to the _Musiciens_ and Hearers, to be so Commodious and pleasant, That
if I would say and dispute, but thus much: That it were to be otherwise
vsed, then it is, I should finde more repreeuers, then I could finde
priuy, or skilfull of my meaning. In thinges therfore euident, and
better knowen, then I can expresse: and so allowed and liked of, (as I
would wish, some other thinges, had the like hap) I will spare to
enlarge my lines any farder, but consequently follow my purpose.
+‡Of Cosmographie‡+, I appointed briefly in this place, to geue you some
intelligence. +Cosmographie, is the whole and perfect description of the
heauenly, and also elementall parte of the world, and their homologall
application, and mutuall collation necessarie.+ This Art, requireth
_Astronomie_, _Geographie_, _Hydrographie_ and _Musike_. Therfore, it is
no small Arte, nor so simple, as in common practise, it is (slightly)
considered. This matcheth Heauen, and the Earth, in one frame, and aptly
applieth parts Correspõdent: So, as, the Heauenly Globe, may (in
practise) be duely described vpon the Geographicall, and Hydrographicall
Globe. And there, for vs to consider an _Æquonoctiall Circle_, _an
Ecliptike line_, _Colures_, _Poles_, _Sterres_ in their true Longitudes,
Latitudes, Declinations, and Verticalitie: also Climes, and Parallels:
and by an _Horizon_ annexed, and reuolution of the earthly Globe (as the
Heauen, is, by the _Primouant_, caried about in 24. æquall Houres) to
learne the Risinges and Settinges of Sterres (of _Virgill_ in his
_Georgikes_: of _Hesiod_: of _Hippocrates_ in his _Medicinall Sphære_,
to Perdicca King of the Macedonians: of _Diocles_, to King _Antigonus_,
and of other famous _Philosophers_ prescribed) a thing necessary, for
due manuring of the earth, for _Nauigation_, for the Alteration of mans
body: being, whole, Sicke, wounded, or brused. By the Reuolution, also,
or mouing of the Globe Cosmographicall, the Rising and Setting of the
Sonne: the Lengthes, of dayes and nightes: the Houres and times (both
night and day) are knowne: with very many other pleasant and necessary
vses: Wherof, some are knowne: but better remaine, for such to know and
vse:
[☞]
who of a sparke of true fire, can make a wonderfull bonfire, by applying
of due matter, duely.