+‡Hypogeiodie‡, is an Arte Mathematicall, demonstratyng, how, vnder the

Sphæricall Superficies of the earth, at any depth, to any perpendicular

line assigned (whose distance from the perpendicular of the entrance:

and the Azimuth, likewise, in respect of the said entrance, is knowen)

certaine way may be præscribed and gone: And how, any way aboue the

Superficies of the earth designed, may vnder earth, at any depth

limited, be kept: goyng alwayes, perpendicularly, vnder the way, on

earth designed: And, contrarywise, Any way, (straight or croked,) vnder

the earth, beyng giuen: vppon the vtface, or Superficies of the earth,

to Lyne out the same: So, as, from the Centre of the earth,

perpendiculars drawen to the Sphæricall Superficies of the earth, shall

precisely fall in the Correspondent pointes of those two wayes. This,

with all other Cases and circumstances herein, and appertenances, this

Arte demonstrateth.+ This Arte, is very ample in varietie of

Conclusions: and very profitable sundry wayes to the Common Wealth. The

occasion of my Inuenting this Arte, was at the request of two Gentlemen,

who had a certaine worke (of gaine) vnder ground: and their groundes did

ioyne ouer the worke: and by reason of the crokednes, diuers depthes,

and heithes of the way vnder ground, they were in doubt, and at

controuersie, vnder whose ground, as then, the worke was. The name onely

(before this) was of me published, _De Itinere Subterraneo_: The rest,

be at Gods will. For Pioners, Miners, Diggers for Mettalls, Stone, Cole,

and for secrete passages vnder ground, betwene place and place (as this

land hath diuerse) and for other purposes, any man may easily perceaue,

both the great fruite of this Arte, and also in this Arte, the great

aide of Geometrie.

+‡Hydragogie‡, demonstrateth the possible leading of Water, by Natures

lawe, and by artificiall helpe, from any head (being a Spring, standing,

or running Water) to any other place assigned.+ Long, hath this Arte

bene in vse: and much thereof written: and very marueilous workes

therein, performed: as may yet appeare, in Italy: by the Ruynes

remaining of the Aqueductes. In other places, of Riuers leading through

the Maine land, Nauigable many a Mile. And in other places, of the

marueilous forcinges of Water to Ascend. which all, declare the great

skill, to be required of him, who should in this Arte be perfecte, for

all occasions of waters possible leading. To speake of the allowance of

the Fall, for euery hundred foote: or of the Ventills (if the waters

labour be farre, and great) I neede not: Seing, at hand (about vs) many

expert men can sufficiently testifie, in effecte, the order: though the

Demonstration of the Necessitie thereof, they know not: Nor yet, if they

should be led, vp and downe, and about Mountaines, from the head of the

Spring: and then, a place being assigned: and of them, to be demaunded,

how low or high, that last place is, in respecte of the head, from which

(so crokedly, and vp and downe) they be come: Perhaps, they would not,

or could not, very redily, or nerely assoyle that question. _Geometrie_

therefore, is necessary to _Hydragogie_. Of the sundry wayes to force

water to ascend, eyther by _Tympane_, _Kettell mills_, _Skrue_,

_Ctesibike_, or such like: in _Vitruuius_, _Agricola_, (and other,)

fully, the maner may appeare. And so, thereby, also be most euident, how

the Artes, of _Pneumatithmie_, _Helicosophie_, _Statike_, _Trochilike_,

and _Menadrie_, come to the furniture of this, in Speculation, and to

the Commoditie of the Common Wealth, in practise.

+‡Horometrie‡, is an Arte Mathematicall, which demõstrateth, how, at all

times appointed, the precise vsuall denominatiõ of time, may be knowen,

for any place assigned.+ These wordes, are smoth and plaine easie

Englishe, but the reach of their meaning, is farther, then you woulde

lightly imagine. Some part of this Arte, was called in olde time,

_Gnomonice_: and of late, _Horologiographia_: and in Englishe, may be

termed, _Dialling_. Auncient is the vse, and more auncient, is the

Inuention. The vse, doth well appeare to haue bene (at the least) aboue

two thousand and three hundred yeare agoe:

[4. Reg. 20.]

in * King _Achaz_ Diall, then, by the Sunne, shewing the distinction of

time. By Sunne, Mone, and Sterres, this Dialling may be performed, and

the precise Time of day or night knowen. But the demonstratiue

delineation of these Dialls, of all sortes, requireth good skill, both

of _Astronomie_, and _Geometrie_ Elementall, Sphæricall, Phænomenall,

and Conikall. Then, to vse the groundes of the Arte, for any regular

Superficies, in any place offred: and (in any possible apt position

therof) theron, to describe (all maner of wayes) how, vsuall howers, may

be (by the _Sunnes_ shadow) truely determined: will be found no sleight

Painters worke. So to Paint, and prescribe the Sunnes Motion, to the

breadth of a heare. In this Feate (in my youth) I Inuented a way, +How

in any Horizontall, Murall, or Æquinoctiall Diall, &c. At all howers

(the Sunne shining) the Signe and Degree ascendent, may be knowen.+

Which is a thing very necessary for the Rising of those fixed Sterres:

whose Operation in the Ayre, is of great might, euidently. I speake no

further, of the vse hereof. Bur forasmuch as, Mans affaires require

knowledge of Times & Momentes, when, neither Sunne, Mone, or Sterre, can

be sene: Therefore, by Industrie Mechanicall, was inuented, first, how,

by Water, running orderly, the Time and howers might be knowen: whereof,

the famous _Ctesibius_, was Inuentor: a man, of _Vitruuius_, to the Skie

(iustly) extolled. Then, after that, by Sand running, were howers

measured: Then, by _Trochilike_ with waight: And of late time, by

_Trochilike_ with Spring: without waight. All these, by Sunne or Sterres

direction (in certaine time) require ouersight and reformation,

according to the heauenly Æquinoctiall Motion: besides the inæqualitie

of their owne Operation. There remayneth (without parabolicall meaning

herein) among the Philosophers,

[A perpetuall Motion.]

a more excellent, more commodious, and more marueilous way, then all

these: of hauing the motion of the Primouant (or first æquinoctiall

motion,) by Nature and Arte, Imitated: which you shall (by furder search

in waightier studyes) hereafter, vnderstand more of. And so, it is tyme

to finish this Annotation, of Tymes distinction, vsed in our common, and

priuate affaires: The commoditie wherof, no man would want, that can

tell, how to bestow his tyme.

+‡Zographie‡, is an Arte Mathematicall, which teacheth and

demonstrateth, how, the Intersection of all visuall Pyramides, made by

any playne assigned, (the Centre, distance, and lightes, beyng

determined) may be, by lynes, and due propre colours, represented.+ A

notable Arte, is this: and would require a whole Volume, to declare the

property thereof: and the Commodities ensuyng. Great skill of

_Geometrie_, _Arithmetike_, _Perspectiue_, and _Anthropographie_, with

many other particular Artes, hath the _Zographer_, nede of, for his

perfection. For, the most excellent Painter, (who is but the propre

Mechanicien, & Imitator sensible, of the Zographer) hath atteined to

such perfection, that Sense of Man and beast, haue iudged thinges

painted, to be things naturall, and not artificiall: aliue, and not

dead. This Mechanicall Zographer (commonly called the Painter) is

meruailous in his skill: and seemeth to haue a certaine diuine power:

As, of frendes absent, to make a frendly, present comfort: yea, and of

frendes dead, to giue a continuall, silent presence: not onely with vs,

but with our posteritie, for many Ages. And so procedyng, Consider, How,

in Winter, he can shew you, the liuely vew of Sommers Ioy, and riches:

and in Sommer, exhibite the countenance of Winters dolefull State, and

nakednes. Cities, Townes, Fortes, Woodes, Armyes, yea whole Kingdomes

(be they neuer so farre, or greate) can he, with ease, bring with him,

home (to any mans Iudgement) as Paternes liuely, of the thinges

rehearsed. In one little house, can he, enclose (with great pleasure of

the beholders,) the portrayture liuely, of all visible Creatures, either

on earth, or in the earth, liuing: or in the waters lying, Creping,

slyding, or swimming: or of any foule, or fly, in the ayre flying. Nay,

in respect of the Starres, the Skie, the Cloudes: yea, in the shew of

the very light it selfe (that Diuine Creature) can he match our eyes

Iudgement, most nerely. What a thing is this? thinges not yet being, he

can represent so, as, at their being, the Picture shall seame (in maner)

to haue Created them. To what Artificer, is not Picture, a great

pleasure and Commoditie? Which of them all, will refuse the Direction

and ayde of Picture? The Architect, the Goldsmith, and the Arras Weauer:

of Picture, make great account. Our liuely Herbals, our portraitures of

birdes, beastes, and fishes: and our curious Anatomies, which way, are

they most perfectly made, or with most pleasure, of vs beholden? Is it

not, by Picture onely? And if Picture, by the Industry of the Painter,

be thus commodious and meruailous: what shall be thought of _Zographie_,

the Scholemaster of Picture, and chief gouernor? Though I mencion not

_Sculpture_, in my Table of Artes Mathematicall: yet may all men

perceiue, How, that _Picture_ and _Sculpture_, are Sisters germaine: and

both, right profitable, in a Commõ wealth. and of _Sculpture_, aswell as

of Picture, excellent Artificers haue written great bokes in

commendation. Witnesse I take, of _Georgio Vasari_, _Pittore Aretino_:

of _Pomponius Gauricus_: and other. To these two Artes, (with other,) is

a certaine od Arte, called _Althalmasat_, much beholdyng: more, then the

common _Sculptor_, _Entayler_, _Keruer_, _Cutter_, _Grauer_, _Founder_,

or _Paynter (&c)_ know their Arte, to be commodious.

[An objection.]

+‡Architecture‡+, to many may seme not worthy, or not mete, to be

reckned among the _Artes Mathematicall_. To whom, I thinke good, to giue

some account of my so doyng. Not worthy, (will they say,) bycause it is

but for building, of a house, Pallace, Church, Forte, or such like,

grosse workes. And you, also, defined the _Artes Mathematicall_, to be

such, as dealed with no Materiall or corruptible thing: and also did

demonstratiuely procede in their faculty, by Number or Magnitude. First,

[The Answer.]

you see, that I count, here, _Architecture_, among those _Artes

Mathematicall_, which are Deriued from the Principals: and you know,

that such, may deale with Naturall thinges, and sensible matter. Of

which, “some draw nerer, to the Simple and absolute Mathematicall

Speculation, then other do.

[☞]

And though, the _Architect_ procureth, enformeth, & directeth, the

_Mechanicien_, to handworke, & the building actuall, of house, Castell,

or Pallace, and is chief Iudge of the same: yet, with him selfe (as

chief _Master_ and _Architect_,) remaineth the Demonstratiue reason and

cause, of the Mechaniciens worke: in Lyne, plaine, and Solid: by

_Geometricall_, _Arithmeticall_, _Opticall_, _Musicall_,

_Astronomicall_, _Cosmographicall_” (& to be brief) by all the former

Deriued _Artes Mathematicall_, and other Naturall Artes, hable to be

confirmed and stablished. If this be so: then, may you thinke, that

_Architecture_, hath good and due allowance, in this honest Company of

_Artes Mathematicall_ Deriuatiue. I will, herein, craue Iudgement of two

most perfect _Architectes_: the one, being _Vitruuius_, the Romaine: who

did write ten bookes thereof, to the Emperour _Augustus_ (in whose daies

our Heauenly Archemaster, was borne): and the other, _Leo Baptista

Albertus_, a Florentine: who also published ten bookes therof.

_Architectura_ (sayth _Vitruuius_) _est Scientia pluribus disciplinis &

varijs eruditionibus ornata: cuius Iudicio probantur omnia, quæ ab

cæteris Artificibus perficiuntur opera._ That is. +Architecture, is a

Science garnished with many doctrines & diuerse instructions: by whose

Iudgement, all workes, by other workmen finished, are Iudged.+ It

followeth. _Ea nascitur ex Fabrica, & Ratiocinatione. &c. Ratiocinatio

autem est, quæ, res fabricatas, Solertia ac ratione proportionis,

demonstrare at[que] explicare potest. +Architecture, groweth of Framing,

and Reasoning. &c. Reasoning, is that, which of thinges framed, with

forecast, and proportion: can make demonstration, and manifest

declaration.+_ Againe. _Cùm, in omnibus enim rebus, tùm maximè etiam in

Architectura, hæc duo insunt: quod significatur, & quod significat.

Significatur proposita res, de qua dicitur: hanc autem Significat

Demonstratio, rationibus doctrinarum explicata. +Forasmuch as, in all

thinges: therefore chiefly in Architecture, these two thinges are: the

thing signified: and that which signifieth. The thing propounded,

whereof we speake, is the thing Signified. But Demonstration, expressed

with the reasons of diuerse doctrines, doth signifie the same thing.+_

After that. _Vt literatus sit, peritus Graphidos, eruditus Geometriæ, &

Optices non ignarus: instructus Arithmetica: historias complures

nouerit, Philosophos diligenter audiuerit: Musicam sciuerit: Medicinæ

non sit ignarus, responsa Iurisperitorũ nouerit: Astrologiam, Cæli[que]

rationes cognitas habeat. +An Architect+_ (sayth he) +_ought to

vnderstand Languages, to be skilfull of Painting, well instructed in

Geometrie, not ignorant of Perspectiue, furnished with Arithmetike, haue

knowledge of many histories, and diligently haue heard Philosophers,

haue skill of Musike, not ignorant of Physike, know the aunsweres of

Lawyers, and haue Astronomie, and the courses Cælestiall, in good

knowledge._+ He geueth reason, orderly, wherefore all these Artes,

Doctrines, and Instructions, are requisite in an excellent _Architect_.

And (for breuitie) omitting the Latin text, thus he hath. +_Secondly, it

is behofefull for an Architect to haue the knowledge of Painting: that

he may the more easilie fashion out, in patternes painted, the forme of

what worke he liketh. And Geometrie, geueth to Architecture many helpes:

and first teacheth the Vse of the Rule, and the Cumpasse: wherby

(chiefly and easilie) the descriptions of Buildinges, are despatched in

Groundplats: and the directions of Squires, Leuells, and Lines.

Likewise, by Perspectiue, the Lightes of the heauen, are well led, in

the buildinges: from certaine quarters of the world. By Arithmetike, the

charges of Buildinges are summed together: the measures are expressed,

and the hard questions of Symmetries, are by Geometricall Meanes and

Methods discoursed on. &c. Besides this, of the Nature of thinges (which

in Greke is called φυσιολογία) Philosophie doth make declaration. Which,

it is necessary, for an Architect, with diligence to haue learned:

because it hath many and diuers naturall questions: as specially, in

Aqueductes. For in their courses, leadinges about, in the leuell ground,

and in the mountinges, the naturall Spirites or breathes are ingendred

diuers wayes: The hindrances, which they cause, no man can helpe, but

he, which out of Philosophie, hath learned the originall causes of

thinges. Likewise, who soeuer shall read Ctesibius, or Archimedes

bookes, (and of others, who haue written such Rules) can not thinke, as

they do: vnlesse he shall haue receaued of Philosophers, instructions in

these thinges. And Musike he must nedes know: that he may haue

vnderstanding, both of Regular and Mathematicall Musike: that he may

temper well his Balistes, Catapultes, and Scorpions. &c. Moreouer, the

Brasen Vessels, which in Theatres, are placed by Mathematicall order, in

ambries, vnder the steppes: and the diuersities of the soundes (which

y^e Grecians call ηχεῖα) are ordred according to Musicall Symphonies &

Harmonies: being distributed in y^e Circuites, by Diatessaron, Diapente,

and Diapason. That the conuenient voyce, of the players sound, whẽ it

came to these preparations, made in order, there being increased: with

y^t increasing, might come more cleare & pleasant, to y^e eares of the

lokers on. &c. And of Astronomie, is knowẽ y^e East, West, South, and

North. The fashion of the heauen, the Æquinox, the Solsticie, and the

course of the sterres. Which thinges, vnleast one know: he can not

perceiue, any thyng at all, the reason of Horologies. Seyng therfore

this ample Science, is garnished, beautified and stored, with so many

and sundry skils and knowledges: I thinke, that none can iustly account

them selues Architectes, of the suddeyne. But they onely, who from their

childes yeares, ascendyng by these degrees of knowledges, beyng fostered

vp with the atteynyng of many Languages and Artes, haue wonne to the

high Tabernacle of Architecture. &c. And to whom Nature hath giuen such

quicke Circumspection, sharpnes of witt, and Memorie, that they may be

very absolutely skillfull in Geometrie, Astronomie, Musike, and the rest

of the Artes Mathematicall: Such, surmount and passe the callyng, and

state, of Architectes:

[A Mathematicien.]

and are become Mathematiciens. &c. And they are found, seldome. As, in

tymes past, was Aristarchus Samius: Philolaus, and Archytas, Tarentynes:

Apollonius Pergęus: Eratosthenes Cyreneus: Archimedes, and Scopas,

Syracusians. Who also, left to theyr posteritie, many Engines and

Gnomonicall workes: by numbers and naturall meanes, inuented and

declared._+

Thus much, and the same wordes (in sense) in one onely Chapter of this

Incõparable _Architect Vitruuius_, shall you finde. And if you should,

but take his boke in your hand, and slightly loke thorough it, you would

say straight way:

[Vitruuius.]

This is _Geometrie_, _Arithmetike_, _Astronomie_, _Musike_,

_Anthropographie_, _Hydragogie_, _Horometrie_. _&c_. and (to cõclude)

the Storehouse of all workmãship. Now, let vs listen to our other Iudge,

our Florentine, _Leo Baptista_: and narrowly consider, how he doth

determine of _Architecture_. _Sed ante[que] vltra progrediar. &c. +But

before I procede any further +_(sayth he) +_I thinke, that I ought to

expresse, what man I would haue to bee allowed an Architect. For, I will

not bryng in place a Carpenter: as though you might Compare him to the

Chief Masters of other Artes. For the hand of the Carpenter, is the

Architectes Instrument._+

[VVho is an Architect.]

+_But I will appoint the Architect to be “that man, who hath the skill,

(by a certaine and meruailous meanes and way,) both in minde and

Imagination to determine and also in worke to finish: what workes so

euer, by motion of waight, and cuppling and framyng together of bodyes,

may most aptly be Commodious for the worthiest Vses of Man.” And that he

may be able to performe these thinges, he hath nede of atteynyng and

knowledge of the best, and most worthy thynges. &c. The whole Feate of

Architecture in buildyng, consisteth in Lineamentes, and in Framyng. And

the whole power and skill of Lineamentes, tendeth to this: that the

right and absolute way may be had, of Coaptyng and ioyning Lines and

angles: by which, the face of the buildyng or frame, may be comprehended

and concluded. And it is the property of Lineamentes, to prescribe vnto

buildynges, and euery part of them, an apt place, & certaine nũber:

a worthy maner, and a semely order: that, so, y^e whole forme and figure

of the buildyng, may rest in the very Lineamentes. &c. And we may

prescribe in mynde and imagination the whole formes, *

[* The Immaterialitie of perfect Architecture.]

all material stuffe beyng secluded. Which point we shall atteyne, by

Notyng and forepointyng the angles, and lines, by a sure and certaine

direction and connexion. Seyng then, these thinges, are thus:_+

[What, Lineament is.]

+_Lineamente, shalbe the certaine and constant prescribyng, conceiued in

mynde: made in lines and angles: and finished with a learned minde and

wyt._+ “We thanke you Master _Baptist_, that you haue so aptly brought

your Arte, and phrase therof, to haue some Mathematicall perfection:

[Note.]

by certaine order, nũber, forme, figure, and _Symmetrie_ mentall:” all

naturall & sensible stuffe set a part. Now, then, it is euident, (Gentle

reader) how aptely and worthely, I haue preferred _Architecture_, to be

bred and fostered vp in the Dominion of the pereles _Princesse_,

_Mathematica_: and to be a naturall Subiect of hers. And the name of

_Architecture_, is of the principalitie, which this Science hath, aboue

all other Artes. And _Plato_ affirmeth, the _Architect_ to be _Master_

ouer all, that make any worke. Wherupon, he is neither Smith, nor

Builder: nor, separately, any Artificer: but the Hed, the Prouost, the

Directer, and Iudge of all Artificiall workes, and all Artificers. For,

the true _Architect_, is hable to teach, Demonstrate, distribute,

describe, and Iudge all workes wrought. And he, onely, searcheth out the

causes and reasons of all Artificiall thynges. Thus excellent, is

_Architecture_: though few (in our dayes) atteyne thereto: yet may not

the Arte, be otherwise thought on, then in very dede it is worthy. Nor

we may not, of auncient Artes, make new and imperfect Definitions in our

dayes: for scarsitie of Artificers: No more, than we may pynche in, the

Definitions of _Wisedome_, or _Honestie_, or of _Frendeshyp_ or of

_Iustice_. No more will I consent, to Diminish any whit, of the

perfection and dignitie, (by iust cause) allowed to absolute

_Architecture_. Vnder the Direction of this Arte, are thre principall,

necessary _Mechanicall Artes_. Namely, _Howsing_, _Fortification_, and

_Naupegie_. _Howsing_, I vnderstand, both for Diuine Seruice, and Mans

common vsage: publike, and priuate. Of _Fortification_ and _Naupegie_,

straunge matter might be told you: But perchaunce, some will be tyred,

with this Bederoll, all ready rehearsed: and other some, will nycely nip

my grosse and homely discoursing with you: made in post hast: for feare

you should wante this true and frendly warnyng, and tast giuyng, of the

_Power Mathematicall_. Lyfe is short, and vncertaine: Tymes are

perilouse: &c. And still the Printer awayting, for my pen staying: All

these thinges, with farder matter of Ingratefulnes, giue me occasion to

passe away, to the other Artes remainyng, with all spede possible.

+The Arte of ‡Nauigation‡, demonstrateth how, by the shortest good way,

by the aptest Directiõ, & in the shortest time, a sufficient Ship,

betwene any two places (in passage Nauigable,) assigned: may be

cõducted: and in all stormes, & naturall disturbances chauncyng, how, to

vse the best possible meanes, whereby to recouer the place first

assigned.+ What nede, the _Master Pilote_, hath of other Artes, here

before recited, it is easie to know: as, of _Hydrographie_,

_Astronomie_, _Astrologie_, and _Horometrie_. Presupposing continually,

the common Base, and foundacion of all: namely _Arithmetike_ and

_Geometrie_. So that, he be hable to vnderstand, and Iudge his own

necessary Instrumentes, and furniture Necessary: Whether they be

perfectly made or no: and also can, (if nede be) make them, hym selfe.

As Quadrantes, The Astronomers Ryng, The Astronomers staffe, The

Astrolabe vniuersall. An Hydrographicall Globe. Charts Hydrographicall,

true, (not with parallell Meridians). The Common Sea Compas: The Compas

of variacion: The Proportionall, and Paradoxall Compasses

[Anno. 1559.]

(of me Inuented, for our two Moscouy Master Pilotes, at the request of

the Company) Clockes with spryng: houre, halfe houre, and three houre

Sandglasses: & sundry other Instrumẽtes: And also, be hable, on Globe,

or Playne to describe the Paradoxall Compasse: and duely to vse the

same, to all maner of purposes, whereto it was inuented. And also, be

hable to Calculate the Planetes places for all tymes.

Moreouer, with Sonne Mone or Sterre (or without) be hable to define the

Longitude & Latitude of the place, which he is in: So that, the

Longitude & Latitude of the place, from which he sayled, be giuen: or by

him, be knowne. whereto, appertayneth expert meanes, to be certified

euer, of the Ships way. &c. And by foreseing the Rising, Settyng,

Nonestedyng, or Midnightyng of certaine tempestuous fixed Sterres: or

their Coniunctions, and Anglynges with the Planetes, &c. he ought to

haue expert coniecture of Stormes, Tempestes, and Spoutes: and such lyke

Meteorologicall effectes, daungerous on Sea. For (as _Plato_ sayth,)

_Mutationes, opportunitates[que] temporum presentire, non minus rei

militari, quàm Agriculturæ, Nauigationi[que] conuenit. +To foresee the

alterations and opportunities of tymes, is conuenient, no lesse to the

Art of Warre, then to Husbandry and Nauigation.+_ And besides such

cunnyng meanes, more euident tokens in Sonne and Mone, ought of hym to

be knowen: such as (the Philosophicall Poëte) _Virgilius_ teacheth, in

hys _Georgikes_. Where he sayth,

[Sidenote: Georgic. 1.]

_Sol quo[que] & exoriens & quum se condet in vndas,

Signa dabit, Solem certissima signa sequuntur. &c.

-------- Nam sæpe videmus,

Ipsius in vultu varios errare colores.

Cæruleus, pluuiam denunciat, igneus Euros.

Sin maculæ incipient rutilo immiscerier igni,

Omnia tum pariter vento, nimbis[que] videbis

Feruere: non illa quisquam me nocte per altum

Ire, ne[que] a terra moueat conuellere funem. &c.

Sol tibi signa dabit. Solem quis dicere falsum

Audeat? -------- &c._

The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara · 第 6 / 8 段