Selected quad for the lemma: truth_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
truth_n	advantage_n	frame_v	great_a	15	3	2.0729	3	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A00429	The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed; Elements. English	Euclid.; Dee, John, 1527-1608.; Candale, François de Foix, comte de, 1502-1594.; Billingsley, Henry, Sir, d. 1606.	1570 (1570)	STC 10560; ESTC S106699	1,020,889	884

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 cā 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 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 It differreth from the Feate Tacticall De acic●us 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 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 contrary wise 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 wil be 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 em●nations 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 thing● in l●ght 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 roūd Globe or Sphere beyng farre of to be a flat and plaine Circle and so likewise iudgeth a plaine Square to be roūd 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

VIRESCIT VULNERE VERITAS THE ELEMENTS OF GEOMETRIE of the most auncient Philosopher EVCLIDE of Megara Faithfully now first translated into the Englishe toung by H. Billingsley Citizen of London Whereunto are annexed certaine Scholics Annotations and Inuentions of the best Mathematicians both of time past and i● this our age With a very fruitfull Praeface made by M. I. d ee specifying the chiefe Mathematicall Sciēces what they are and wherunto commodious● where also are disclosed certaine new Secrets Mathematicall and Mech●●icall vntill these our daies greatly missed Imprinted at London by Iohn Daye The Translator to the Reader THere is gentle Reader nothing the word of God onely set apart which so much beautifieth and adorneth the soule and minde of mā as doth the knowledge of good artes and sciences as the knowledge of naturall and morall Philosophie The one setteth before our eyes the creatures of God both in the heauens aboue and in the earth beneath in which as in a glasse we beholde the exceding maiestie and wisedome of God in adorning and beautifying them as we see in geuing vnto them such wonderfull and manifolde proprieties and naturall workinges and that so diuersly and in such varietie farther in maintaining and conseruing them continually whereby to praise and adore him as by S. Paule we are taught The other teacheth vs rules and preceptes of vertue how in common life amongest men we ought to walke vprightly what dueties pertaine to our selues what pertaine to the gouernment or good order both of an housholde and also of a citie or common wealth The reading likewise of histories conduceth not a litle to the adorning of the soule minde of man a studie of all men cōmended by it are seene and knowen the artes and doinges of infinite wise men gone before vs In histories are contained infinite examples of heroicall vertues to be of vs followed and horrible examples of vices to be of vs eschewed Many other artes also there are which beautifie the minde of man but of all other none do more garnishe beautifie it then those artes which are called Mathematicall Vnto the knowledge of which no man can attaine without the perfecte knowledge and instruction of the principles groundes and Elementes of Geometrie But perfectly to be instructed in them requireth diligent studie and reading of olde auncient authors Amongest which none for a beginner is to be preferred before the most auncient Philosopher Euclide of Megara For of all others he hath in a true methode and iuste order gathered together whatsoeuer any before him had of these Elementes written inuenting also and adding many thinges of his owne wherby he hath in due forme accomplished the arte first geuing definitions principles groundes wherof he deduceth his Propositions or conclusions in such wonderfull wise that that which goeth before is of necessitie required to the proufe of that which followeth So that without the diligent studie of Euclides Elementes it is impossible to attaine vnto the perfecte knowledge of Geometrie and consequently of any of the other Mathematicall sciences Wherefore considering the want lacke of such good authors hitherto in our Englishe tounge lamenting also the negligence and lacke of zeale to their countrey in those of our nation to whom God hath geuen both knowledge also abilitie to translate into our tounge and to publishe abroad such good authors and bookes the chiefe instrumentes of all learninges seing moreouer that many good wittes both of gentlemen and of others of all degrees much desirous and studious of these artes and seeking for them as much as they can sparing no paines and yet frustrate of their intent by no meanes attaining to that which they seeke I haue for their sakes with some charge great trauaile faithfully translated into our vulgare toūge set abroad in Print this booke of Euclide Whereunto I haue added easie and plaine declarations and examples by figures of the definitions In which booke also ye shall in due place finde manifolde additions Scholies Annotations and Inuentions which I haue gathered out of many of the most famous chiefe Mathematicies both of old time and in our age as by diligent reading it in course ye shall well perceaue The fruite and gaine which I require for these my paines and trauaile shall be nothing els but onely that thou gentle reader will gratefully accept the same and that thou mayest thereby receaue some profite and moreouer to excite and stirre vp others learned to do the like to take paines in that behalfe By meanes wherof our Englishe tounge shall no lesse be enriched with good Authors then are other straunge tounges as the Dutch French Italian and Spanishe in which are red all good authors in a manner found amongest the Grekes or Latines Which is the chiefest cause that amongest thē do florishe so many cunning and skilfull men in the inuentions of straunge and wonderfull thinges as in these our daies we see there do Which fruite and gaine if I attaine vnto it shall encourage me hereafter in such like sort to translate and set abroad some other good authors both pertaining to religion as partly I haue already done and also pertaining to the Mathematicall Artes. Thus gentle reader farewell TO THE VNFAINED LOVERS of truthe and constant Studentes of Noble Sciences IOHN d ee of London hartily wisheth grace from heauen and most prosperous successe in all their honest attemptes and exercises DIuine Plato the great Master of many worthy Philosophers and the constant auoucher and pithy perswader of Vnum Bonum and Ens in his Schole and Academie sundry times besides his ordinary Scholers was visited of a certaine kinde of men allured by the noble fame of Plato and the great commendation of hys profound and profitable doctrine But when such Hearers after long harkening to him perceaued that the drift of his discourses issued out to conclude this Vnum Bonum and Ens to be Spirituall Infinite AEternall Omnipotent c. Nothyng beyng alledged or expressed How worldly goods how worldly dignitie how health Strēgth or Iustines of body nor yet the meanes how a merue●lous sensible and bodyly blysse and felicitie hereafter might be atteyned Straightway the fantasies of those hearers were dampt their opinion of Plato was clene chaunged yea his doctrine was by them despised and his schole no more of ●hem visited Which thing his Scholer Aristotle narrowly cōsidering founde the cause therof to be For that they had no forwarnyng and information in generall whereto his doctrine tended For so might they haue had occasion either to haue forborne his schole hauntyng if they then had misliked his Scope and purpose or constantly to haue continued therin to their full satisfaction if such finall scope intent had ben to their desire Wherfore Aristotle euer after that vsed in brief to forewarne his owne Scholers and hearers both of what matter and also to what ende he tooke in hand to speake or teach While I

word or two hereafter shall be sayd How Immateriall and free from all matter Number is who doth not perceaue ye● who doth not wonderfully wōder at it For neither pure Element nor Aristoteles Quinta Essentia is hable to serue for Number as his propre matter Nor yet the puritie and simplenes of Substance Spirituall or Angelicall will be found propre enough thereto And therefore the great godly Philosopher Anitius Boetius sayd Omnia quaecunque a primaua rerum na●●ra constructa sunt Numerorum videntur ratione formata Hoc enim fuit principale in animo Conditoris Exemplar That is All thinges which from the very first originall be●ng of thinges haue bene framed and made do appeare to be Formed by the reason of Numbers For this was the principall example or patterne in the minde of the Creator O comfortable alluremen● O rauishing perswasion to deale with a Science whose Subiect i● so Auncient so pure so excellent so surmounting all creatures so vsed of the Almighty and incomprehensible wisdome of the Creator in the distinct creation of all creatures● in all their distinct partes properties natures and vertues by order and most absolute number brought from Nothing to the Formalitie of their being and state By Numbers propertie therefore of vs by all possible meanes to the perfection of the Science learned we may both winde and draw our selues into the inward and deepe search and v●w of all creatures distinct vertues natures properties and Former And also farder arise clime ascend and mount vp with Speculatiue winges in spirit to behold in the Glas of Creation the Forme of Formes the Exemplar Number of all thinges Numerable both visible and inuisible● mortall and immortall Corporall and Spirituall Part of this profound and diuine Science had Ioachim the Prophesier atteyned vnto by Numbers Formall Naturall and Rationall forseyng concludyng and forshewyng great particular euents long before their comming His bookes yet remainyng hereof are good profe And the noble Earle of Mirandula besides that a sufficient witnesse that Ioachim in his prophesies proceded by no other way then by Numbers Formall And this Earle hym selfe in Rome set vp 900. Conclusions in all kinde of Sciences openly to be disputed of and among the rest in his Conclusions Mathematicall in the eleuenth Conclusion hath in Latin this English sentence By Numbers a way is had to the searchyng out aud vnderstandyng of euery thyng hable to be knowen For the verifying of which Conclusion I promise to aunswere to the 74. Quaestions vnder written by the way of Numbers Which Cōclusions I omit here to rehearse aswell auoidyng superfluous prolixitie as bycause Ioannes Picus workes are commonly had But in any case I would wish that those Conclusions were red diligently and perceiued of such as are earnest Obseruers and Considerers of the constant law of nūbers which is planted in thyngs Naturall and Supernaturall and is prescribed to all Creatures inuiolably to be kept For so besides many other thinges in those Conclusions to be marked it would apeare how sincerely within my boundes I disclose the wonderfull mysteries by numbers to be atteyned vnto Of my former wordes easy it is to be gathered that Number hath a treble state One in the Creator an other in euery Creature in respect of his complete constitution and the third in Spirituall and Angelicall Myndes and in the Soule of mā In the first and third state Number is termed Number Numbryng But in all Creatures otherwise Number is termed Nūber Numbred And in our Soule Nūber beareth such a swaye and hath such an affinitie therwith that some of the old Philosophers taught Mans Soule to be a Number mouyng it selfe And in dede in vs though it be a very Accident yet such an Accident it is that before all Creatures it had perfect beyng in the Creator Sempiternally Number Numbryng therfore is the discretion discerning and distincting of thinges But in God the Creator This discretion in the beginnyng produced orderly and distinctly all thinges For his Numbryng then was his Creatyng of all thinges And his Continuall Numbryng of all thinges is the Conseruation of them in being And where and when he will lacke an Vnit there and then that particular thyng shal be Discreated Here I stay But our Seuerallyng distinctyng and Numbryng createth nothyng● but of Multitude considered maketh certaine and distinct determination And albeit these thynges be waighty and truthes of great importance yet by the infinite goodnes of the Almighty Ternarie Artificiall Methods and easy wayes are made by which the zelous Philosopher may wyn nere this Riuerish Ida ● this Mountayne of Contemplation and more then Contemplation And also though Number be a thyng so Immateriall so diuine and aeternall yet by degrees by litle and litle stretchyng forth and applying some likenes of it as first to thinges Spirituall and then bryngyng it lower to thynges sensibly perceiued as of a momentanye sounde iterated then to the least thynges that may be seen numerable And at length most grossely to a multitude of any corporall thynges seen or felt and so of these grosse and sensible thynges we are trayned to learne a certaine Image or likenes of numbers and to vse Arte in them to our pleasure and proffit So grosse is our conuersation and dull is our apprehension while mortall Sense in vs ruleth the common wealth of our litle world Hereby we say Three Lyons are three or a Ternarie Three Egles are three or a Ternarie Which Ternaries are eche the Vnion knot and Vniformitie of three discrete and distinct Vnits That is we may in eche Ternarie thrise seuerally pointe and shew a part One One and One. Where in Numbryng we say One two Three But how farre these visible Ones do differre from our Indiuisible Vnits in pure Arithmetike principally considered no man is ignorant Yet from these grosse and materiall thynges may we be led vpward by degrees so informyng our rude Imagination toward the coceiuyng of Numbers absolutely Not supposing nor admixtyng any thyng created Corporall or Spirituall to support conteyne or represent those Numbers imagined that at length we may be hable to finde the number of our owne name gloriously exemplified and registred in the booke of the Trinitie most blessed and aeternall But farder vnderstand that vulgar Practisers haue Numbers otherwise in sundry Considerations and extend their name farder then to Numbers whose least part is an Vnit. For the common Logist Reckenmaster or Arithmeticien in hys vsing of Numbers of an Vnit imagineth lesse partes● and calleth them Fractions As of an Vnit he maketh an halfe and thus noteth it ½ and so of other infinitely diuerse partes of an Vnit Yea and farder hath Fractions of Fractions c. And forasmuch as Addition Substraction Multiplication Diuision and Extraction of Rotes are the chief and sufficient partes of Arithmetike which is the Science that demonstrateth the properties of Numbers and all operatiōs in numbers to be performed

Creatures of their Naturall Vertue being most mighty most beneficiall to all elementall Generation Corr●p●ion and the appa●●●nances● and most Harmonious in thei● Monarchie For which thinges being ●nowen and modestly vsed we might highly ●nd continually glorifie God with the princely Prophet saying The Heauens declare the Glorie of God who made the Heauēs in his wisedome who made the Sonne for to haue dominion of the day the Mone and Sterres to haue dominion of the nyght whereby Day to day ●●●●reth tal●●● and night to night declareth knowledge Prayse him all ye St●rr●s and Light. Amen IN order now foloweth of Statike somewhat to say what we meane by ●hat name● and what 〈…〉 doth on 〈◊〉 Art depend Statike is an Arte Mathematicall which demonstra●●th the causes of heauynes and lightnes of all thynges and of motions and properties to heauynes and lightnes belonging● And for asmuch as by the Bilanx or Balance as the chief sensible Instrument Experience of these demonstrations may be had we call this Art Statike that is the Experimentes of the Balance Oh that men wist what proffit all maner of wayes by this Arte might grow to the hable examiner and diligent practiser Thou onely knowest all thinges precisely O God who hast made weight and Balance thy Iudgement who hast created all thinges in Number Waight and Measure and hast wayed the mountaines and hils in a Balance who hast peysed in thy hand both Heauen and earth We therfore warned by the Sacred word to Consider thy Creatures and by that consideration to wynne a glyms as it were or shaddow of perceiuerance that thy wisedome might and goodnes is infinite and vnspeakable in thy Creatures declared And being farder aduertised by thy mercifull goodnes that three principall wayes were of the vsed in Creation of all thy Creatures namely Number Waight and Measure And for as much as of Number and Measure the two Artes auncient famous and to humaine vses most necessary are all ready sufficiently knowen and extant This third key we beseche thee through thy accustomed goodnes that it may come to the nedefull and sufficient knowledge of such thy Seruauntes as in thy workemanship would gladly finde thy true occasions purposely of the vsed whereby we should glorifie thy name and shew forth to the weaklinges in faith thy wondrous wisedome and Goodnes Amen Meruaile nothing at this pang godly frend you Gentle and zelous Student An other day perchaunce you will perceiue what occasion moued me Here as now I will giue you some ground and withall some shew of certaine commodities by this Arte arising And bycause this Arte is rare my wordes and practises might be to darke vnleast you had some light holden before the matter and that best will be in giuing you out of Archimedes demonstrations a few principal Conclusions as foloweth 1. The Superficies of euery Liquor by it selfe consistyng and in quyet is Sphaericall the centre whereof is the same which is the centre of the Earth 2. If Solide Magnitudes being of the same bignes or quātitie that any Liquor is and hauyng also the same Waight be let downe into the same Liquor they will settle downeward so that no parte of them shall be aboue the Superficies of the Liquor and yet neuertheles they will not sinke vtterly downe or drowne 3. If any Solide Magnitude beyng Lighter then a Liquor be let downe into the same Liquor it will settle downe so farre into the same Liquor that so great a quantitie of that Liquor as is the parte of the Solid Magnitude settled dow●e into the same Liquor ● is in Waight aequall to the waight of the whole Solid Magni●ude 4. Any Solide Magnitude Lighter then a Liquor forced downe into the same Liquor will moue vpward with so great a power by how much the Liquor hauyng aequall quantitie to the whole Magnitude is heauyer then the same Magnitude 5. Any Solid Magnitude heauyer then a Liquor beyng let downe into the same Liquor will sinke downe vtterly And wil be in that Liquor Lighter by so much as is the waight or heauynes of the Liquor hauing bygnes or quantitie aequall to the Solid Magnitude 6. If any Solide Magnitude Lighter then a Liquor be let downe into the same Liquor the waight of the same Magnitude will be to the Waight of the Liquor Which is aequall in quantitie to the whole Magnitude in that proportion that the parte of the Magnitude settled downe is to the whole Magnitude BY these verities great Errors may be reformed in Opinion of the Naturall Motion of thinges Light and Heauy Which errors are in Naturall Philosophie almost of all mē allowed to much trusting to Authority and false Suppositions As Of any two bodyes the heauyer to moue downward faster then the lighter This error is not first by me Noted but by one Iohn Baptist de Benedictis The chief of his propositions is this which seemeth a Paradox If there be two bodyes of one forme and of one kynde aequall in quantitie or vnaequall they will moue by aequall space in aequall tyme So that both theyr mouynges be in ayre or both in water or in any one Middle Hereupon in the feate of Gunnyng certaine good discourses otherwise may receiue great amendement and furderance In the entended purpose also allowing somwhat to the imperfection of Nature not aunswerable to the precisenes of demonstration Moreouer by the foresaid propositions wisely vsed The Ayre the water the Earth the Fire may be nerely knowen how light or heauy they are Naturally in their ●●●gned partes or in the whole And then to thinges Elementall turning your practise you may deale for the proportion of the Elementes in the thinges Compounded Then to the proportions of the Humours in Man their waightes and the waight of his bones and flesh c. Than by waight to haue consideration of the Force of man any maner of way in whole or in part Then may you of Ships water drawing diuersly in the Sea and in fresh water haue pleasant consideration and of waying vp of any thing sonken in Sea or in fresh water c. And to lift vp your head a loft by waight you may as precisely as by any instrument els measure the Diameters of Sonne and Mone c. Frende I pray you way these thinges with the iust Balance of Reason And you will finde Meruailes vpon Meruailes And esteme one Drop of Truth yea in Naturall Philosophie more worth then whole Libraries of Opinions vndemonstrated or not aunswering to Natures Law and your experience Leauing these thinges thus I will giue you two or three light practises to great purpose● and so finish my Annotation Staticall In Mathematicall matters by the Mechaniciens ayde we will behold here the Commodity of waight Make a Cube of any one Vniforme and through like heauy stuffe of the same Stuffe make a Sphaere or Globe precisely of a Diameter aequall to the Radicall side of the Cube Your stuffe may