This textincludes characters that require UTF-8 (Unicode) file encoding:ã ẽ ĩ õ ũ (vowels with overline, shown here as a tilde)ἐίπερ γὰρ ἀδικεῖμ χρὴ(Greek, mainly in the introduction)If any of these characters do not display properly—in particular, if the diacritic does not appear directly above the letter—or if the apostrophes and quotation marks in this paragraph appear as garbage, you may have an incompatible browser or unavailable fonts. First, make sure that the browser’s “character set” or “file encoding” is set to Unicode (UTF-8). You may also need to change your browser’s default font.Unless otherwise noted, spelling, punctuation and capitalization are unchanged. Text in sans-serif type was originally printed in blackletter (“Gothic”, Old English). Typographical errors are marked in the text withmouse-hover popups. Transliteration of single Greek words and short phrases is shown in the same way; the longer Greek passages from the introduction are given at the end of the e-text.The book does not have page numbers. Instead, it labeled the recto (odd) pages of the first few leaves of each 8-page signature. These will appear in the right margin as A.i., A.ij., A.iij.... Page numbers in brackets, including all verso (v) pages, were added by the transcriber.Any problems or explanations too long or complicated to fit into apopupare noted either in a separate paragraph or at theend of the e-text.Full ContentsPrinciples of GeometryConclusionsAxioms(“Grauntable Requestes”and “Common Sentences”)TheoremsGeometries verdicteAll fresshe fine wittes by me are filed,All grosse dull wittes wishe me exiled:Thoughe no mannes witte reiect will I,Yet as they be, I wyll them trye.The argumentes of the foure bookesThe first booke declareth the definitions of the termes and names vsed in Geometry, with certaine of the chiefe grounds whereon the arte is founded. And then teacheth those conclusions, which may serue diuersely in al workes Geometricall.The second booke doth sette forth the Theoremes, (whiche maye be called approued truthes) seruinge for the due knowledge and sure proofe of all conclusions and workes in Geometrye.The third booke intreateth of diuers formes, and sondry protractions thereto belonging, with the vse of certain conclusions.The fourth booke teacheth the right order of measuringe all platte formes, and bodies also, by reson Geometricall.Contents(added by transcriber)Title Page(above)Arguments of the Four Books(above)First Book:To the Gentle ReaderDedication to King Edward VIPreface to the First BookThe Principles of GeometryConclusions 1–46Second Book:Title PagePreface to the Second BookGrantable RequestsCommon SentencesTheorems 1–77Text of Decorative HeadersTranscriber’s NotesTO THE GENTLE READER.Excvse me, gentle reder if oughte be amisse, straung paths ar not trodẽ al truly at the first: the way muste needes be comberous, wher none hathe gone before. Where no man hathe geuen light, lighte is it to offend, but when the light is shewed ones, light is it to amende. If my light may so light some other, to espie and marke my faultes, I wish it may so lighten thẽ, that they may voide offence. Of staggeringe and stomblinge, and vnconstaunt turmoilinge: often offending, and seldome amending, such vices to eschewe, and their fine wittes to shew that they may winne the praise, and I to hold the candle, whilest they their glorious works with eloquence sette forth, so cunningly inuented, so finely indited, that my bokes maie seme worthie to occupie no roome. For neither is mi wit so finelie filed, nother mi learning so largly lettred, nother yet mi laiser so quiet and vncõbered, that I maie perform iustlie so learned a laboure or accordinglie to accomplishe sohaulte an enforcement, yet maie I thinke thus: This candle did I light: this light haue I kindeled: that learned men maie se, to practise their pennes, their eloquence to aduaunce, to register their names in the booke of memorie I drew the platte rudelie, whereon thei maie builde, whom god hath indued with learning and liuelihod. For liuing by laboure doth learning so hinder, that learning serueth liuinge, whiche is a peruers trade. Yet as carefull familie shall cease hir cruell callinge, and suffre anie laiser to learninge to repaire, I will not cease from trauaile the pathe so to trade, that finer wittes maie fashion them selues with such glimsinge dull light, a more complete woorke at laiser to finisshe, with inuencion agreable, and aptnes of eloquence.And this gentle reader I hartelie protest where erroure hathe happened I wisshe it redrest.see end of textIt is not vnknowen to youre maiestie, moste soueraigne lorde, what great disceptacion hath been amongest the wyttie men of all nacions, for the exacte knoweledge of true felicitie, bothe what it is, and wherein it consisteth: touchynge whiche thyng, their opinions almoste were as many in numbre, as were the persons of them, that either disputed or wrote thereof. But and if the diuersitie of opinions in the vulgar sort for placyng of their felicitie shall be considered also, the varietie shall be found so great, and the opinions so dissonant, yea plainly monsterouse, that no honest witte would vouchesafe to lose time in hearyng thẽ, or rather (as I may saie) no witte is of so exact remembrance, that can consider together the monsterouse multitude of them all. And yet not withstãdyng this repugnant diuersitie, in two thynges do they all agree. First all do agre, that felicitie is and ought to be the stop and end of all their doynges, so that he that hath a full desire to any thyng how so euer it be estemed of other mẽ, yet he estemeth him self happie, if he maie obtain it: and contrary waies vnhappie if he can not attaine it. And therfore do all men put their whole studie to gette that thyng, wherin they haue perswaded them self that felicitiedoth consist. Wherfore some whiche put their felicitie in fedyng their bellies, thinke no pain to be hard, nor no dede to be vnhonest, that may be a meanes to fill that foule panche. Other which put their felicitie in play and ydle pastimes, iudge no time euill spent, that is employed thereabout: nor no fraude vnlawfull that may further their winning. If I should particularly ouerrũne but the common sortes of men, which put their felicitie in their desires, it wold make a great boke of it self. Therfore wyl I let them al go, and conclude as Ibegan, Thatall men employ their whole endeuour to that thing, wherin thei thinke felicitie tostand. whichethyng who so listeth to mark exactly, shall be able to espie and iudge the natures of al men, whose conuersaciõ he doth know, though thei vse great dissimulacion to colour their desires, especially whẽ they perceiue other men to mislyke that which thei so much desire: For no mã wold gladly haue his appetite improued. And herof cõmeth that secõndething wherin al agree, that euery man would most gladly win all other men to his sect, and to make thẽ of his opinion, and as far as he dare, will dispraise all other mens iudgemẽtes, and praise his own waies only, onles it be when he dissimuleth, and that for the furtherãce of his own purpose. And this propertie also doth geue great light to the full knowledge of mens natures, which as all men ought to obserue, so princes aboue other haue most cause to mark for sundrie occasions which may lye them on, wherof I shall not nede to speke any farther, consideryng not only the greatnes of wit, and exactnes of iudgement whiche god hath lent vnto your highnes person, but also yemost graue wisdom and profoũd knowledge of your maiesties most honorable coũcel, by whõ your highnes may so sufficiently vnderstãd all thinges conuenient, that lesse shal it nede to vnderstand by priuate readying, but yet not vtterly to refuse to read as often as occasion may serue, for bokes dare speake, when men feare to displease. But toreturne agayne to my firste matter, if none other good thing maie be lerned at their maners, which so wrõgfully place their felicity, in so miserable a cõditiõ (that while they thinke them selfes happy, their felicitie must nedes seme vnluckie, to be by them so euill placed) yet this may men learn at them, by those .ij. spectacles to espye the secrete natures and dispositions of others, whiche thyng vnto a wise man is muche auailable. And thus will I omit this great tablement of vnhappie hap, and wil come to .iij. other sortes of a better degre, wherof the one putteth felicitie to consist in power and royaltie. The second sorte vnto power annexeth worldly wisdome, thinkyng him full happie, that could attayn those two, wherby he might not onely haue knowledge in all thynges, but also power to bryng his desires to ende. The thyrd sort estemeth true felicitie to consist in wysdom annexed with vertuouse maners, thinkyng that they can take harme of nothyng, if they can with theirwysedome*ouercome all vyces. Of the firste of thosethreesortes there hath been a great numbre in all ages, yea many mightie kinges and great gouernoures which cared not greately howe they myght atchieue their pourpose, so that they dyd preuayle: nor did not take any greatter care for gouernance, then to kepe the people in onely feare of them,Whose commonsentence was alwaies this:Oderint dum metuant. And what good successe suche menne had, all histories doe report. Yet haue they not wanted excuses: yea Iulius Cæsar (whiche in dede was of the second sorte) maketh a kynde of excuse by his common sentence, for them of that fyrste sorte, for he was euer woonte to saie:ἐίπερ γὰρ ἀδικεῖμ χρὴ, τυραννΐδος περῒ κάλλιστομ ἀδικεῖμ, τ’ ἄλλα δ’ ἐυσεβεῖμ χρεῶμ. Whiche sentence I wysshe had neuer been learned out of Grecia. But now to speake of the second sort, of whiche there hathe been verye many also, yet for this present time amongest them all, I wyll take the exaumples ofkynge Phylippe of Macedonie, and of Alexander his sonne, that valiaunt conquerour. First of kinge Phylip it appeareth by his letter sente vnto Aristotle that famous philosopher, that he more delited in the birthe of his sonne, for the hope of learning and good education, that might happen to him by the said Aristotle, then he didde reioyse in the continuaunce of his succession, for these were his wordes and his whole epistle, worthye to bee remembred and registred euery where.Φΐλιππος Αριστοτέλει χαίρειμ.ἔσθι μοι γεγονότα ὑομ. πολλὴμ οὖμ τοῖσ θεοῖσ χάριμ ἔχω, ὀυχ ὅυτωσ ἐπῒ τῆ γεννήσει του παιδόσ, ὡσ ἐπῒ τῷ κατὰ τὴμ σὴμ ἡλικῒαμ αὐτόμ γεγονέναι ἐλπΐζω γὰρ αὐτὸμ ὑπὸ σοῦ γραφέντα καὶ παιδευθέντα ἄξιομ ἔσεσθαι καὶ ἑιμῶμ καὶ τῆς τῶμ τραγμάτωμ διαδοχῆσ.That is thus in sense,Philip vnto Aristotle sendeth gretyng.You shall vnderstande, that I haue a sonne borne, for whiche cause I yelde vnto God moste hartie thankes, not so muche for the byrthe of the childe, as that it was his chaunce to be borne in your tyme. For my trust is, that he shall be so brought vp and instructed by you, that he shall become worthie not only to be named our sonne, but also to be the successour of our affayres.And his good desire was not all vayne, for it appered that Alexander was neuer so busied with warres (yet was he neuer out of moste terrible battaile) but that in the middes thereof he had in remembraunce his studies, and caused in all countreies as he went, all strange beastes,fowles and fisshes, to be taken and kept for the ayd of that knowledg, which he learned of Aristotle: And also to be had with him alwayes a greate numbre of learned men. And in the moste busye tyme of all his warres against Darius kinge of Persia, when he harde that Aristotle had putte forthe certainebookesof suche knowledge wherein he hadde before studied, hee was offended with Aristotle, and wrote to hym this letter.Ἄλέζανδρος Αρισοτέλει εὖ πράττειμ.Ὂυκ ὀρθῶσ ἐπόιησασ ἐκδοὺσ τοὺσ ἀκροαματικόυσ τῶμ λόγωμ,τΐνι γὰρ διοισομην ἡμεῖσ τῶμ ἄλλωμ, ἐι καθ’ οὕσ ἐπαιδεύθημεν λόγουσ, ὅυτοι πάντωμ ἔσονταιν κοινόι, ἐγὼ δὲ βουλοί μημ ἅμ ταῖσ περι τὰ ἄριστα ἐμπειρΐαισ, ἢ τὰισ δυνάμεσι διαφέριμ. ἔρρωσο. that isAlexander vnto Aristotle sendeth greeting.You haue not doone well, to put forthe those bookes of secrete phylosophy intituled,ακροαματικοι.For wherin shall we excell other, yf that knowledge that wee haue studied, shall be made commen to all other men, namely sithe our desire is to excelle other men in experience and knowledge, rather then in power and strength. Farewell.By whyche lettre it appeareth that hee estemed learninge and knowledge aboue power of men. And the like iudgement did he vtter, when he beheld the state of Diogenes Linicus, adiudginge it the beste state next to his owne, so that he said: If I were not Alexander, I wolde wishe to be Diogenes. Whereby apeareth, how he esteemed learning, and what felicity he putte therin, reputing al the worlde saue him selfe to be inferiour to Diogenes. And bi al coniecturs, Alexander did esteme Diogenes one of them whiche contemned the vaine estimation of the disceitfull world, and put his whole felicity in knowledg of vertue, and practise of the same, though some reportethat he knew more vertue then he folowed: But whatso euer he was, it appeareth that Socrates and Plato and many other did forsake their liuings and sel away their patrimony, to the intent to seeke and trauaile for learning, which examples I shall not need to repete to your Maiesty, partly for that your highnes doth often reade them and other lyke, and partly sith your maiesty hath at hand such learned schoolemaysters, which can much better thẽ I, declare them vnto your highnes, and that more largely also then the shortenes of thys epistle will permit. But thys may I yet adde, that King Salomon whose renoume spred so farre abroad, was very greatlye estemed for his wonderfull power and exceading treasure, but yet much more was he estemed for his wisdom.And him selfe doth bear witnes, that wisedom is better then pretiousstones . yeaall thinges that can be desired ar not to be compared to it. But what needeth to alledge one sentence of him, whose bookes altogither do none other thing, then set forth the praise of wisedom & knowledg? And his father kingDauidioynethuertuousconuersacion and knowledg togither, as the summe of perfection and chief felicity. Wherfore I maye iustelye conclude, that true felicity doth consist in wisdome and vertu. Then if wisdome be as Cicero defineth it,Diuinarum atq; humanarum rerum scientia, then ought all men to trauail for knowledg in matters both of religion and humaine docrine, if he shall be counted wyse, and able to attaine true felicitie: But as the study of religious matters is most principall, so I leue it for this time to them that better can write of it then I can. And for humaine knowledge thys wil I boldly say, that who soeuer wyll attain true iudgment therein, must not only trauail in yeknowledg of the tungs, but must also before al other arts, taste of the mathematical sciences, specially Arithmetike and Geometry, without which it is not possible to attayn full knowledg in any art. Which may sufficiẽtly by gathered by Aristotle not õly in his bookesof demonstration (whiche can not be vnderstand without Geometry) but also in all his other workes. And before him Plato his maister wrote this sentence on his schole house dore.Αγεομέτρητοσ ὀυδὲισ ἐισΐτω.. Let no man entre here (saith he) without knowledg in Geometry. Wherfore moste mighty prince, as your most excellent Maiesty appeareth to be borne vnto most perfect felicity, not only by reasõ that God moued with the long prayers of this realme, did send your highnes as moste comfortable inheritour to the same, but also in that your Maiesty was borne in the time of such skilful schoolmaisters & learned techers, as your highnes doth not a little reioyse in, and profite by them in all kind of vertu & knowledg. Amõgst which is that heauẽly knowledg most worthely to be praised, wherbi the blindnes of errour & superstition is exiled, & good hope cõceiued that al the sedes & fruts therof, with all kindes of vice & iniquite, wherby vertu is hindered, & iustice defaced, shal be cleanextrirpedand rooted out of this realm, which hope shal increase more and more, if it may appear that learning be estemed & florish within this realm. And al be it the chief learnĩg be the diuine scriptures, which instruct the mind principally, & nexte therto the lawes politike, which most specially defẽd the right of goodes, yet is it not possible that those two can long be wel vsed, if that ayde want that gouerneth health and expelleth sicknes, which thing is done by Physik, & these require the help of the vij. liberall sciences, but of none more then of Arithmetik and Geometry, by which not only great thinges ar wrought touchĩg accõptes in al kinds, & in suruaiyng & measuring of lãdes, but also al arts depend partly of thẽ, & building which is most necessary can not be wtout them, which thing cõsidering, moued me to help to serue your maiesty in this point as wel as other wais, & to do what mai be in me, ytnot õly thei which studi prĩcipalli for lernĩg, mai haue furderãce bi mi poore help, butalso those whiche haue no tyme to trauaile for exacter knowlege, may haue some helpe to vnderstand in those Mathematicall artes, in whiche as I haue all readye set forth sumwhat of Arithmetike, so god willing I intend shortly to setforth a more exacter worke therof. And in the meane ceason for a taste of Geometry, I haue sette forthe this small introduction, desiring your grace not so muche to beholde the simplenes of the woorke, in comparison to your Maiesties excellencye,as to fauour the edition thereof, for the ayde of your humble subiectes, which shal thinke them selues more and more dayly bounden to your highnes, if when they shall perceaue your graces desyre to haue theym profited in all knowledge and vertue. And I for my poore ability considering your Maiesties studye for the increase of learning generally through all your highenes dominions, and namely in the vniuersities of Oxforde and Camebridge, as I haue an earnest good will as far as my simple seruice and small knowledg will suffice, to helpe toward the satisfiyng of your graces desire, so if I shall perceaue that my seruice may be to your maiesties contẽtacion, I wil not only put forth the other two books, whiche shoulde haue beene sette forth with these two, yf misfortune had not hindered it, but also I wil set forth other bookes of more exacter arte, bothe in the Latine tongue and also in the Englyshe, whereof parte bee all readye written, and newe instrumentes to theym deuised, and the residue shall bee eanded with all possible speede. I was boldened to dedicate this booke of Geometrye vnto your Maiestye, not so muche bycause it is the firste that euer was sette forthe in Englishe, and therefore for the noueltye a straunge presente, but for that I was perswaded, that suche a wyse prince doothe desire to haue a wise sorte of subiectes. For it is a kynges chiefe reioysinge and glory, if his subiectes be riche insubstaunce, and wytty in knowledge: and contraryewaies nothyng can bee more greuouse to a noble kyng, then that his realme should be other beggerly or full of ignoraunce: But as god hath geuen your grace a realme bothe riche in commodities and also full of wyttie men, so I truste by the readyng of wyttie artes (whiche be as the whette stones of witte) they muste needes increase more and more in wysedome, and peraduenture fynde some thynge towarde the ayde of their substaunce, whereby your grace shall haue newe occasion to reioyce, seyng your subiectes to increase in substance or wisdom, or in both. And thei again shal hauenew and newcauses to pray for yourmaiestie, perceiuyngso graciouse a mind towarde their benefite. And I truste (as I desire) that a great numbre of gentlemen, especially about the courte, whiche vnderstand not the latin tong, or els for the hardnesse of the mater could not away with other mens writyng, will fall in trade with this easie forme of teachyng in their vulgar tong, and so employe some of their tyme in honest studie, whiche were wont to bestowe most part of their time in triflyng pastime: Forvndoubtedlyiftheymean other your maiesties seruice, other their own wisdome, they will be content to employ some tyme aboute this honest and wittie exercise. For whose encouragemẽt to the intent they maie perceiue what shall be the vse of this science, I haue not onely written somewhat of the vse of Geometrie, but also I haue annexed to this boke the names and brefe argumentes of those other bokes whiche I will set forth hereafter, and that as shortly as it shall appeare vnto your maiestie by coniecture of their diligent vsyng of this first boke, that they wyll vse well the other bokes also. In the meane ceason, and at all times I wil be a continuall petitioner, that god may work in all english hartes an ernest mynde to all honest exercises, wherby thei may serue the better your maiestie andthe realm. And for your highnes I besech the most mercifull god, as he hath most fauourably sent you vnto vs, as our chefe comforter in earthe, so that he will increase your maiestie daiely in all vertue and honor with moste prosperouse successe, and augment in vs your most humble subiectes, true loue to godward, and iust obedience toward your highnes with all reuerence and subiection.At London the .xxviij. daie of Ianuarie. M. D. L I.Your maiesties moste humble seruantand obedient subiect,Robert Recorde.
This textincludes characters that require UTF-8 (Unicode) file encoding:ã ẽ ĩ õ ũ (vowels with overline, shown here as a tilde)ἐίπερ γὰρ ἀδικεῖμ χρὴ(Greek, mainly in the introduction)If any of these characters do not display properly—in particular, if the diacritic does not appear directly above the letter—or if the apostrophes and quotation marks in this paragraph appear as garbage, you may have an incompatible browser or unavailable fonts. First, make sure that the browser’s “character set” or “file encoding” is set to Unicode (UTF-8). You may also need to change your browser’s default font.Unless otherwise noted, spelling, punctuation and capitalization are unchanged. Text in sans-serif type was originally printed in blackletter (“Gothic”, Old English). Typographical errors are marked in the text withmouse-hover popups. Transliteration of single Greek words and short phrases is shown in the same way; the longer Greek passages from the introduction are given at the end of the e-text.The book does not have page numbers. Instead, it labeled the recto (odd) pages of the first few leaves of each 8-page signature. These will appear in the right margin as A.i., A.ij., A.iij.... Page numbers in brackets, including all verso (v) pages, were added by the transcriber.Any problems or explanations too long or complicated to fit into apopupare noted either in a separate paragraph or at theend of the e-text.Full ContentsPrinciples of GeometryConclusionsAxioms(“Grauntable Requestes”and “Common Sentences”)Theorems
This textincludes characters that require UTF-8 (Unicode) file encoding:
ã ẽ ĩ õ ũ (vowels with overline, shown here as a tilde)
ἐίπερ γὰρ ἀδικεῖμ χρὴ(Greek, mainly in the introduction)
If any of these characters do not display properly—in particular, if the diacritic does not appear directly above the letter—or if the apostrophes and quotation marks in this paragraph appear as garbage, you may have an incompatible browser or unavailable fonts. First, make sure that the browser’s “character set” or “file encoding” is set to Unicode (UTF-8). You may also need to change your browser’s default font.
Unless otherwise noted, spelling, punctuation and capitalization are unchanged. Text in sans-serif type was originally printed in blackletter (“Gothic”, Old English). Typographical errors are marked in the text withmouse-hover popups. Transliteration of single Greek words and short phrases is shown in the same way; the longer Greek passages from the introduction are given at the end of the e-text.
The book does not have page numbers. Instead, it labeled the recto (odd) pages of the first few leaves of each 8-page signature. These will appear in the right margin as A.i., A.ij., A.iij.... Page numbers in brackets, including all verso (v) pages, were added by the transcriber.
Any problems or explanations too long or complicated to fit into apopupare noted either in a separate paragraph or at theend of the e-text.
Full ContentsPrinciples of GeometryConclusionsAxioms(“Grauntable Requestes”and “Common Sentences”)Theorems
Geometries verdicteAll fresshe fine wittes by me are filed,All grosse dull wittes wishe me exiled:Thoughe no mannes witte reiect will I,Yet as they be, I wyll them trye.
All fresshe fine wittes by me are filed,All grosse dull wittes wishe me exiled:Thoughe no mannes witte reiect will I,Yet as they be, I wyll them trye.
All fresshe fine wittes by me are filed,All grosse dull wittes wishe me exiled:Thoughe no mannes witte reiect will I,Yet as they be, I wyll them trye.
All fresshe fine wittes by me are filed,
All grosse dull wittes wishe me exiled:
Thoughe no mannes witte reiect will I,
Yet as they be, I wyll them trye.
The argumentes of the foure bookesThe first booke declareth the definitions of the termes and names vsed in Geometry, with certaine of the chiefe grounds whereon the arte is founded. And then teacheth those conclusions, which may serue diuersely in al workes Geometricall.The second booke doth sette forth the Theoremes, (whiche maye be called approued truthes) seruinge for the due knowledge and sure proofe of all conclusions and workes in Geometrye.The third booke intreateth of diuers formes, and sondry protractions thereto belonging, with the vse of certain conclusions.The fourth booke teacheth the right order of measuringe all platte formes, and bodies also, by reson Geometricall.
The first booke declareth the definitions of the termes and names vsed in Geometry, with certaine of the chiefe grounds whereon the arte is founded. And then teacheth those conclusions, which may serue diuersely in al workes Geometricall.
The second booke doth sette forth the Theoremes, (whiche maye be called approued truthes) seruinge for the due knowledge and sure proofe of all conclusions and workes in Geometrye.
The third booke intreateth of diuers formes, and sondry protractions thereto belonging, with the vse of certain conclusions.
The fourth booke teacheth the right order of measuringe all platte formes, and bodies also, by reson Geometricall.
Contents(added by transcriber)Title Page(above)Arguments of the Four Books(above)First Book:To the Gentle ReaderDedication to King Edward VIPreface to the First BookThe Principles of GeometryConclusions 1–46Second Book:Title PagePreface to the Second BookGrantable RequestsCommon SentencesTheorems 1–77Text of Decorative HeadersTranscriber’s Notes
Title Page(above)
Arguments of the Four Books(above)
First Book:To the Gentle ReaderDedication to King Edward VIPreface to the First BookThe Principles of GeometryConclusions 1–46
Second Book:Title PagePreface to the Second BookGrantable RequestsCommon SentencesTheorems 1–77
Text of Decorative Headers
Transcriber’s Notes
TO THE GENTLE READER.Excvse me, gentle reder if oughte be amisse, straung paths ar not trodẽ al truly at the first: the way muste needes be comberous, wher none hathe gone before. Where no man hathe geuen light, lighte is it to offend, but when the light is shewed ones, light is it to amende. If my light may so light some other, to espie and marke my faultes, I wish it may so lighten thẽ, that they may voide offence. Of staggeringe and stomblinge, and vnconstaunt turmoilinge: often offending, and seldome amending, such vices to eschewe, and their fine wittes to shew that they may winne the praise, and I to hold the candle, whilest they their glorious works with eloquence sette forth, so cunningly inuented, so finely indited, that my bokes maie seme worthie to occupie no roome. For neither is mi wit so finelie filed, nother mi learning so largly lettred, nother yet mi laiser so quiet and vncõbered, that I maie perform iustlie so learned a laboure or accordinglie to accomplishe sohaulte an enforcement, yet maie I thinke thus: This candle did I light: this light haue I kindeled: that learned men maie se, to practise their pennes, their eloquence to aduaunce, to register their names in the booke of memorie I drew the platte rudelie, whereon thei maie builde, whom god hath indued with learning and liuelihod. For liuing by laboure doth learning so hinder, that learning serueth liuinge, whiche is a peruers trade. Yet as carefull familie shall cease hir cruell callinge, and suffre anie laiser to learninge to repaire, I will not cease from trauaile the pathe so to trade, that finer wittes maie fashion them selues with such glimsinge dull light, a more complete woorke at laiser to finisshe, with inuencion agreable, and aptnes of eloquence.And this gentle reader I hartelie protest where erroure hathe happened I wisshe it redrest.
Excvse me, gentle reder if oughte be amisse, straung paths ar not trodẽ al truly at the first: the way muste needes be comberous, wher none hathe gone before. Where no man hathe geuen light, lighte is it to offend, but when the light is shewed ones, light is it to amende. If my light may so light some other, to espie and marke my faultes, I wish it may so lighten thẽ, that they may voide offence. Of staggeringe and stomblinge, and vnconstaunt turmoilinge: often offending, and seldome amending, such vices to eschewe, and their fine wittes to shew that they may winne the praise, and I to hold the candle, whilest they their glorious works with eloquence sette forth, so cunningly inuented, so finely indited, that my bokes maie seme worthie to occupie no roome. For neither is mi wit so finelie filed, nother mi learning so largly lettred, nother yet mi laiser so quiet and vncõbered, that I maie perform iustlie so learned a laboure or accordinglie to accomplishe sohaulte an enforcement, yet maie I thinke thus: This candle did I light: this light haue I kindeled: that learned men maie se, to practise their pennes, their eloquence to aduaunce, to register their names in the booke of memorie I drew the platte rudelie, whereon thei maie builde, whom god hath indued with learning and liuelihod. For liuing by laboure doth learning so hinder, that learning serueth liuinge, whiche is a peruers trade. Yet as carefull familie shall cease hir cruell callinge, and suffre anie laiser to learninge to repaire, I will not cease from trauaile the pathe so to trade, that finer wittes maie fashion them selues with such glimsinge dull light, a more complete woorke at laiser to finisshe, with inuencion agreable, and aptnes of eloquence.
And this gentle reader I hartelie protest where erroure hathe happened I wisshe it redrest.
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It is not vnknowen to youre maiestie, moste soueraigne lorde, what great disceptacion hath been amongest the wyttie men of all nacions, for the exacte knoweledge of true felicitie, bothe what it is, and wherein it consisteth: touchynge whiche thyng, their opinions almoste were as many in numbre, as were the persons of them, that either disputed or wrote thereof. But and if the diuersitie of opinions in the vulgar sort for placyng of their felicitie shall be considered also, the varietie shall be found so great, and the opinions so dissonant, yea plainly monsterouse, that no honest witte would vouchesafe to lose time in hearyng thẽ, or rather (as I may saie) no witte is of so exact remembrance, that can consider together the monsterouse multitude of them all. And yet not withstãdyng this repugnant diuersitie, in two thynges do they all agree. First all do agre, that felicitie is and ought to be the stop and end of all their doynges, so that he that hath a full desire to any thyng how so euer it be estemed of other mẽ, yet he estemeth him self happie, if he maie obtain it: and contrary waies vnhappie if he can not attaine it. And therfore do all men put their whole studie to gette that thyng, wherin they haue perswaded them self that felicitiedoth consist. Wherfore some whiche put their felicitie in fedyng their bellies, thinke no pain to be hard, nor no dede to be vnhonest, that may be a meanes to fill that foule panche. Other which put their felicitie in play and ydle pastimes, iudge no time euill spent, that is employed thereabout: nor no fraude vnlawfull that may further their winning. If I should particularly ouerrũne but the common sortes of men, which put their felicitie in their desires, it wold make a great boke of it self. Therfore wyl I let them al go, and conclude as Ibegan, Thatall men employ their whole endeuour to that thing, wherin thei thinke felicitie tostand. whichethyng who so listeth to mark exactly, shall be able to espie and iudge the natures of al men, whose conuersaciõ he doth know, though thei vse great dissimulacion to colour their desires, especially whẽ they perceiue other men to mislyke that which thei so much desire: For no mã wold gladly haue his appetite improued. And herof cõmeth that secõndething wherin al agree, that euery man would most gladly win all other men to his sect, and to make thẽ of his opinion, and as far as he dare, will dispraise all other mens iudgemẽtes, and praise his own waies only, onles it be when he dissimuleth, and that for the furtherãce of his own purpose. And this propertie also doth geue great light to the full knowledge of mens natures, which as all men ought to obserue, so princes aboue other haue most cause to mark for sundrie occasions which may lye them on, wherof I shall not nede to speke any farther, consideryng not only the greatnes of wit, and exactnes of iudgement whiche god hath lent vnto your highnes person, but also yemost graue wisdom and profoũd knowledge of your maiesties most honorable coũcel, by whõ your highnes may so sufficiently vnderstãd all thinges conuenient, that lesse shal it nede to vnderstand by priuate readying, but yet not vtterly to refuse to read as often as occasion may serue, for bokes dare speake, when men feare to displease. But toreturne agayne to my firste matter, if none other good thing maie be lerned at their maners, which so wrõgfully place their felicity, in so miserable a cõditiõ (that while they thinke them selfes happy, their felicitie must nedes seme vnluckie, to be by them so euill placed) yet this may men learn at them, by those .ij. spectacles to espye the secrete natures and dispositions of others, whiche thyng vnto a wise man is muche auailable. And thus will I omit this great tablement of vnhappie hap, and wil come to .iij. other sortes of a better degre, wherof the one putteth felicitie to consist in power and royaltie. The second sorte vnto power annexeth worldly wisdome, thinkyng him full happie, that could attayn those two, wherby he might not onely haue knowledge in all thynges, but also power to bryng his desires to ende. The thyrd sort estemeth true felicitie to consist in wysdom annexed with vertuouse maners, thinkyng that they can take harme of nothyng, if they can with theirwysedome*ouercome all vyces. Of the firste of thosethreesortes there hath been a great numbre in all ages, yea many mightie kinges and great gouernoures which cared not greately howe they myght atchieue their pourpose, so that they dyd preuayle: nor did not take any greatter care for gouernance, then to kepe the people in onely feare of them,Whose commonsentence was alwaies this:Oderint dum metuant. And what good successe suche menne had, all histories doe report. Yet haue they not wanted excuses: yea Iulius Cæsar (whiche in dede was of the second sorte) maketh a kynde of excuse by his common sentence, for them of that fyrste sorte, for he was euer woonte to saie:ἐίπερ γὰρ ἀδικεῖμ χρὴ, τυραννΐδος περῒ κάλλιστομ ἀδικεῖμ, τ’ ἄλλα δ’ ἐυσεβεῖμ χρεῶμ. Whiche sentence I wysshe had neuer been learned out of Grecia. But now to speake of the second sort, of whiche there hathe been verye many also, yet for this present time amongest them all, I wyll take the exaumples ofkynge Phylippe of Macedonie, and of Alexander his sonne, that valiaunt conquerour. First of kinge Phylip it appeareth by his letter sente vnto Aristotle that famous philosopher, that he more delited in the birthe of his sonne, for the hope of learning and good education, that might happen to him by the said Aristotle, then he didde reioyse in the continuaunce of his succession, for these were his wordes and his whole epistle, worthye to bee remembred and registred euery where.Φΐλιππος Αριστοτέλει χαίρειμ.ἔσθι μοι γεγονότα ὑομ. πολλὴμ οὖμ τοῖσ θεοῖσ χάριμ ἔχω, ὀυχ ὅυτωσ ἐπῒ τῆ γεννήσει του παιδόσ, ὡσ ἐπῒ τῷ κατὰ τὴμ σὴμ ἡλικῒαμ αὐτόμ γεγονέναι ἐλπΐζω γὰρ αὐτὸμ ὑπὸ σοῦ γραφέντα καὶ παιδευθέντα ἄξιομ ἔσεσθαι καὶ ἑιμῶμ καὶ τῆς τῶμ τραγμάτωμ διαδοχῆσ.That is thus in sense,Philip vnto Aristotle sendeth gretyng.You shall vnderstande, that I haue a sonne borne, for whiche cause I yelde vnto God moste hartie thankes, not so muche for the byrthe of the childe, as that it was his chaunce to be borne in your tyme. For my trust is, that he shall be so brought vp and instructed by you, that he shall become worthie not only to be named our sonne, but also to be the successour of our affayres.And his good desire was not all vayne, for it appered that Alexander was neuer so busied with warres (yet was he neuer out of moste terrible battaile) but that in the middes thereof he had in remembraunce his studies, and caused in all countreies as he went, all strange beastes,fowles and fisshes, to be taken and kept for the ayd of that knowledg, which he learned of Aristotle: And also to be had with him alwayes a greate numbre of learned men. And in the moste busye tyme of all his warres against Darius kinge of Persia, when he harde that Aristotle had putte forthe certainebookesof suche knowledge wherein he hadde before studied, hee was offended with Aristotle, and wrote to hym this letter.Ἄλέζανδρος Αρισοτέλει εὖ πράττειμ.Ὂυκ ὀρθῶσ ἐπόιησασ ἐκδοὺσ τοὺσ ἀκροαματικόυσ τῶμ λόγωμ,τΐνι γὰρ διοισομην ἡμεῖσ τῶμ ἄλλωμ, ἐι καθ’ οὕσ ἐπαιδεύθημεν λόγουσ, ὅυτοι πάντωμ ἔσονταιν κοινόι, ἐγὼ δὲ βουλοί μημ ἅμ ταῖσ περι τὰ ἄριστα ἐμπειρΐαισ, ἢ τὰισ δυνάμεσι διαφέριμ. ἔρρωσο. that isAlexander vnto Aristotle sendeth greeting.You haue not doone well, to put forthe those bookes of secrete phylosophy intituled,ακροαματικοι.For wherin shall we excell other, yf that knowledge that wee haue studied, shall be made commen to all other men, namely sithe our desire is to excelle other men in experience and knowledge, rather then in power and strength. Farewell.By whyche lettre it appeareth that hee estemed learninge and knowledge aboue power of men. And the like iudgement did he vtter, when he beheld the state of Diogenes Linicus, adiudginge it the beste state next to his owne, so that he said: If I were not Alexander, I wolde wishe to be Diogenes. Whereby apeareth, how he esteemed learning, and what felicity he putte therin, reputing al the worlde saue him selfe to be inferiour to Diogenes. And bi al coniecturs, Alexander did esteme Diogenes one of them whiche contemned the vaine estimation of the disceitfull world, and put his whole felicity in knowledg of vertue, and practise of the same, though some reportethat he knew more vertue then he folowed: But whatso euer he was, it appeareth that Socrates and Plato and many other did forsake their liuings and sel away their patrimony, to the intent to seeke and trauaile for learning, which examples I shall not need to repete to your Maiesty, partly for that your highnes doth often reade them and other lyke, and partly sith your maiesty hath at hand such learned schoolemaysters, which can much better thẽ I, declare them vnto your highnes, and that more largely also then the shortenes of thys epistle will permit. But thys may I yet adde, that King Salomon whose renoume spred so farre abroad, was very greatlye estemed for his wonderfull power and exceading treasure, but yet much more was he estemed for his wisdom.And him selfe doth bear witnes, that wisedom is better then pretiousstones . yeaall thinges that can be desired ar not to be compared to it. But what needeth to alledge one sentence of him, whose bookes altogither do none other thing, then set forth the praise of wisedom & knowledg? And his father kingDauidioynethuertuousconuersacion and knowledg togither, as the summe of perfection and chief felicity. Wherfore I maye iustelye conclude, that true felicity doth consist in wisdome and vertu. Then if wisdome be as Cicero defineth it,Diuinarum atq; humanarum rerum scientia, then ought all men to trauail for knowledg in matters both of religion and humaine docrine, if he shall be counted wyse, and able to attaine true felicitie: But as the study of religious matters is most principall, so I leue it for this time to them that better can write of it then I can. And for humaine knowledge thys wil I boldly say, that who soeuer wyll attain true iudgment therein, must not only trauail in yeknowledg of the tungs, but must also before al other arts, taste of the mathematical sciences, specially Arithmetike and Geometry, without which it is not possible to attayn full knowledg in any art. Which may sufficiẽtly by gathered by Aristotle not õly in his bookesof demonstration (whiche can not be vnderstand without Geometry) but also in all his other workes. And before him Plato his maister wrote this sentence on his schole house dore.Αγεομέτρητοσ ὀυδὲισ ἐισΐτω.. Let no man entre here (saith he) without knowledg in Geometry. Wherfore moste mighty prince, as your most excellent Maiesty appeareth to be borne vnto most perfect felicity, not only by reasõ that God moued with the long prayers of this realme, did send your highnes as moste comfortable inheritour to the same, but also in that your Maiesty was borne in the time of such skilful schoolmaisters & learned techers, as your highnes doth not a little reioyse in, and profite by them in all kind of vertu & knowledg. Amõgst which is that heauẽly knowledg most worthely to be praised, wherbi the blindnes of errour & superstition is exiled, & good hope cõceiued that al the sedes & fruts therof, with all kindes of vice & iniquite, wherby vertu is hindered, & iustice defaced, shal be cleanextrirpedand rooted out of this realm, which hope shal increase more and more, if it may appear that learning be estemed & florish within this realm. And al be it the chief learnĩg be the diuine scriptures, which instruct the mind principally, & nexte therto the lawes politike, which most specially defẽd the right of goodes, yet is it not possible that those two can long be wel vsed, if that ayde want that gouerneth health and expelleth sicknes, which thing is done by Physik, & these require the help of the vij. liberall sciences, but of none more then of Arithmetik and Geometry, by which not only great thinges ar wrought touchĩg accõptes in al kinds, & in suruaiyng & measuring of lãdes, but also al arts depend partly of thẽ, & building which is most necessary can not be wtout them, which thing cõsidering, moued me to help to serue your maiesty in this point as wel as other wais, & to do what mai be in me, ytnot õly thei which studi prĩcipalli for lernĩg, mai haue furderãce bi mi poore help, butalso those whiche haue no tyme to trauaile for exacter knowlege, may haue some helpe to vnderstand in those Mathematicall artes, in whiche as I haue all readye set forth sumwhat of Arithmetike, so god willing I intend shortly to setforth a more exacter worke therof. And in the meane ceason for a taste of Geometry, I haue sette forthe this small introduction, desiring your grace not so muche to beholde the simplenes of the woorke, in comparison to your Maiesties excellencye,as to fauour the edition thereof, for the ayde of your humble subiectes, which shal thinke them selues more and more dayly bounden to your highnes, if when they shall perceaue your graces desyre to haue theym profited in all knowledge and vertue. And I for my poore ability considering your Maiesties studye for the increase of learning generally through all your highenes dominions, and namely in the vniuersities of Oxforde and Camebridge, as I haue an earnest good will as far as my simple seruice and small knowledg will suffice, to helpe toward the satisfiyng of your graces desire, so if I shall perceaue that my seruice may be to your maiesties contẽtacion, I wil not only put forth the other two books, whiche shoulde haue beene sette forth with these two, yf misfortune had not hindered it, but also I wil set forth other bookes of more exacter arte, bothe in the Latine tongue and also in the Englyshe, whereof parte bee all readye written, and newe instrumentes to theym deuised, and the residue shall bee eanded with all possible speede. I was boldened to dedicate this booke of Geometrye vnto your Maiestye, not so muche bycause it is the firste that euer was sette forthe in Englishe, and therefore for the noueltye a straunge presente, but for that I was perswaded, that suche a wyse prince doothe desire to haue a wise sorte of subiectes. For it is a kynges chiefe reioysinge and glory, if his subiectes be riche insubstaunce, and wytty in knowledge: and contraryewaies nothyng can bee more greuouse to a noble kyng, then that his realme should be other beggerly or full of ignoraunce: But as god hath geuen your grace a realme bothe riche in commodities and also full of wyttie men, so I truste by the readyng of wyttie artes (whiche be as the whette stones of witte) they muste needes increase more and more in wysedome, and peraduenture fynde some thynge towarde the ayde of their substaunce, whereby your grace shall haue newe occasion to reioyce, seyng your subiectes to increase in substance or wisdom, or in both. And thei again shal hauenew and newcauses to pray for yourmaiestie, perceiuyngso graciouse a mind towarde their benefite. And I truste (as I desire) that a great numbre of gentlemen, especially about the courte, whiche vnderstand not the latin tong, or els for the hardnesse of the mater could not away with other mens writyng, will fall in trade with this easie forme of teachyng in their vulgar tong, and so employe some of their tyme in honest studie, whiche were wont to bestowe most part of their time in triflyng pastime: Forvndoubtedlyiftheymean other your maiesties seruice, other their own wisdome, they will be content to employ some tyme aboute this honest and wittie exercise. For whose encouragemẽt to the intent they maie perceiue what shall be the vse of this science, I haue not onely written somewhat of the vse of Geometrie, but also I haue annexed to this boke the names and brefe argumentes of those other bokes whiche I will set forth hereafter, and that as shortly as it shall appeare vnto your maiestie by coniecture of their diligent vsyng of this first boke, that they wyll vse well the other bokes also. In the meane ceason, and at all times I wil be a continuall petitioner, that god may work in all english hartes an ernest mynde to all honest exercises, wherby thei may serue the better your maiestie andthe realm. And for your highnes I besech the most mercifull god, as he hath most fauourably sent you vnto vs, as our chefe comforter in earthe, so that he will increase your maiestie daiely in all vertue and honor with moste prosperouse successe, and augment in vs your most humble subiectes, true loue to godward, and iust obedience toward your highnes with all reuerence and subiection.At London the .xxviij. daie of Ianuarie. M. D. L I.
It is not vnknowen to youre maiestie, moste soueraigne lorde, what great disceptacion hath been amongest the wyttie men of all nacions, for the exacte knoweledge of true felicitie, bothe what it is, and wherein it consisteth: touchynge whiche thyng, their opinions almoste were as many in numbre, as were the persons of them, that either disputed or wrote thereof. But and if the diuersitie of opinions in the vulgar sort for placyng of their felicitie shall be considered also, the varietie shall be found so great, and the opinions so dissonant, yea plainly monsterouse, that no honest witte would vouchesafe to lose time in hearyng thẽ, or rather (as I may saie) no witte is of so exact remembrance, that can consider together the monsterouse multitude of them all. And yet not withstãdyng this repugnant diuersitie, in two thynges do they all agree. First all do agre, that felicitie is and ought to be the stop and end of all their doynges, so that he that hath a full desire to any thyng how so euer it be estemed of other mẽ, yet he estemeth him self happie, if he maie obtain it: and contrary waies vnhappie if he can not attaine it. And therfore do all men put their whole studie to gette that thyng, wherin they haue perswaded them self that felicitiedoth consist. Wherfore some whiche put their felicitie in fedyng their bellies, thinke no pain to be hard, nor no dede to be vnhonest, that may be a meanes to fill that foule panche. Other which put their felicitie in play and ydle pastimes, iudge no time euill spent, that is employed thereabout: nor no fraude vnlawfull that may further their winning. If I should particularly ouerrũne but the common sortes of men, which put their felicitie in their desires, it wold make a great boke of it self. Therfore wyl I let them al go, and conclude as Ibegan, Thatall men employ their whole endeuour to that thing, wherin thei thinke felicitie tostand. whichethyng who so listeth to mark exactly, shall be able to espie and iudge the natures of al men, whose conuersaciõ he doth know, though thei vse great dissimulacion to colour their desires, especially whẽ they perceiue other men to mislyke that which thei so much desire: For no mã wold gladly haue his appetite improued. And herof cõmeth that secõndething wherin al agree, that euery man would most gladly win all other men to his sect, and to make thẽ of his opinion, and as far as he dare, will dispraise all other mens iudgemẽtes, and praise his own waies only, onles it be when he dissimuleth, and that for the furtherãce of his own purpose. And this propertie also doth geue great light to the full knowledge of mens natures, which as all men ought to obserue, so princes aboue other haue most cause to mark for sundrie occasions which may lye them on, wherof I shall not nede to speke any farther, consideryng not only the greatnes of wit, and exactnes of iudgement whiche god hath lent vnto your highnes person, but also yemost graue wisdom and profoũd knowledge of your maiesties most honorable coũcel, by whõ your highnes may so sufficiently vnderstãd all thinges conuenient, that lesse shal it nede to vnderstand by priuate readying, but yet not vtterly to refuse to read as often as occasion may serue, for bokes dare speake, when men feare to displease. But toreturne agayne to my firste matter, if none other good thing maie be lerned at their maners, which so wrõgfully place their felicity, in so miserable a cõditiõ (that while they thinke them selfes happy, their felicitie must nedes seme vnluckie, to be by them so euill placed) yet this may men learn at them, by those .ij. spectacles to espye the secrete natures and dispositions of others, whiche thyng vnto a wise man is muche auailable. And thus will I omit this great tablement of vnhappie hap, and wil come to .iij. other sortes of a better degre, wherof the one putteth felicitie to consist in power and royaltie. The second sorte vnto power annexeth worldly wisdome, thinkyng him full happie, that could attayn those two, wherby he might not onely haue knowledge in all thynges, but also power to bryng his desires to ende. The thyrd sort estemeth true felicitie to consist in wysdom annexed with vertuouse maners, thinkyng that they can take harme of nothyng, if they can with theirwysedome*ouercome all vyces. Of the firste of thosethreesortes there hath been a great numbre in all ages, yea many mightie kinges and great gouernoures which cared not greately howe they myght atchieue their pourpose, so that they dyd preuayle: nor did not take any greatter care for gouernance, then to kepe the people in onely feare of them,Whose commonsentence was alwaies this:Oderint dum metuant. And what good successe suche menne had, all histories doe report. Yet haue they not wanted excuses: yea Iulius Cæsar (whiche in dede was of the second sorte) maketh a kynde of excuse by his common sentence, for them of that fyrste sorte, for he was euer woonte to saie:ἐίπερ γὰρ ἀδικεῖμ χρὴ, τυραννΐδος περῒ κάλλιστομ ἀδικεῖμ, τ’ ἄλλα δ’ ἐυσεβεῖμ χρεῶμ. Whiche sentence I wysshe had neuer been learned out of Grecia. But now to speake of the second sort, of whiche there hathe been verye many also, yet for this present time amongest them all, I wyll take the exaumples ofkynge Phylippe of Macedonie, and of Alexander his sonne, that valiaunt conquerour. First of kinge Phylip it appeareth by his letter sente vnto Aristotle that famous philosopher, that he more delited in the birthe of his sonne, for the hope of learning and good education, that might happen to him by the said Aristotle, then he didde reioyse in the continuaunce of his succession, for these were his wordes and his whole epistle, worthye to bee remembred and registred euery where.
ἔσθι μοι γεγονότα ὑομ. πολλὴμ οὖμ τοῖσ θεοῖσ χάριμ ἔχω, ὀυχ ὅυτωσ ἐπῒ τῆ γεννήσει του παιδόσ, ὡσ ἐπῒ τῷ κατὰ τὴμ σὴμ ἡλικῒαμ αὐτόμ γεγονέναι ἐλπΐζω γὰρ αὐτὸμ ὑπὸ σοῦ γραφέντα καὶ παιδευθέντα ἄξιομ ἔσεσθαι καὶ ἑιμῶμ καὶ τῆς τῶμ τραγμάτωμ διαδοχῆσ.
That is thus in sense,
You shall vnderstande, that I haue a sonne borne, for whiche cause I yelde vnto God moste hartie thankes, not so muche for the byrthe of the childe, as that it was his chaunce to be borne in your tyme. For my trust is, that he shall be so brought vp and instructed by you, that he shall become worthie not only to be named our sonne, but also to be the successour of our affayres.
And his good desire was not all vayne, for it appered that Alexander was neuer so busied with warres (yet was he neuer out of moste terrible battaile) but that in the middes thereof he had in remembraunce his studies, and caused in all countreies as he went, all strange beastes,fowles and fisshes, to be taken and kept for the ayd of that knowledg, which he learned of Aristotle: And also to be had with him alwayes a greate numbre of learned men. And in the moste busye tyme of all his warres against Darius kinge of Persia, when he harde that Aristotle had putte forthe certainebookesof suche knowledge wherein he hadde before studied, hee was offended with Aristotle, and wrote to hym this letter.
Ὂυκ ὀρθῶσ ἐπόιησασ ἐκδοὺσ τοὺσ ἀκροαματικόυσ τῶμ λόγωμ,τΐνι γὰρ διοισομην ἡμεῖσ τῶμ ἄλλωμ, ἐι καθ’ οὕσ ἐπαιδεύθημεν λόγουσ, ὅυτοι πάντωμ ἔσονταιν κοινόι, ἐγὼ δὲ βουλοί μημ ἅμ ταῖσ περι τὰ ἄριστα ἐμπειρΐαισ, ἢ τὰισ δυνάμεσι διαφέριμ. ἔρρωσο. that is
You haue not doone well, to put forthe those bookes of secrete phylosophy intituled,ακροαματικοι.For wherin shall we excell other, yf that knowledge that wee haue studied, shall be made commen to all other men, namely sithe our desire is to excelle other men in experience and knowledge, rather then in power and strength. Farewell.
By whyche lettre it appeareth that hee estemed learninge and knowledge aboue power of men. And the like iudgement did he vtter, when he beheld the state of Diogenes Linicus, adiudginge it the beste state next to his owne, so that he said: If I were not Alexander, I wolde wishe to be Diogenes. Whereby apeareth, how he esteemed learning, and what felicity he putte therin, reputing al the worlde saue him selfe to be inferiour to Diogenes. And bi al coniecturs, Alexander did esteme Diogenes one of them whiche contemned the vaine estimation of the disceitfull world, and put his whole felicity in knowledg of vertue, and practise of the same, though some reportethat he knew more vertue then he folowed: But whatso euer he was, it appeareth that Socrates and Plato and many other did forsake their liuings and sel away their patrimony, to the intent to seeke and trauaile for learning, which examples I shall not need to repete to your Maiesty, partly for that your highnes doth often reade them and other lyke, and partly sith your maiesty hath at hand such learned schoolemaysters, which can much better thẽ I, declare them vnto your highnes, and that more largely also then the shortenes of thys epistle will permit. But thys may I yet adde, that King Salomon whose renoume spred so farre abroad, was very greatlye estemed for his wonderfull power and exceading treasure, but yet much more was he estemed for his wisdom.And him selfe doth bear witnes, that wisedom is better then pretiousstones . yeaall thinges that can be desired ar not to be compared to it. But what needeth to alledge one sentence of him, whose bookes altogither do none other thing, then set forth the praise of wisedom & knowledg? And his father kingDauidioynethuertuousconuersacion and knowledg togither, as the summe of perfection and chief felicity. Wherfore I maye iustelye conclude, that true felicity doth consist in wisdome and vertu. Then if wisdome be as Cicero defineth it,Diuinarum atq; humanarum rerum scientia, then ought all men to trauail for knowledg in matters both of religion and humaine docrine, if he shall be counted wyse, and able to attaine true felicitie: But as the study of religious matters is most principall, so I leue it for this time to them that better can write of it then I can. And for humaine knowledge thys wil I boldly say, that who soeuer wyll attain true iudgment therein, must not only trauail in yeknowledg of the tungs, but must also before al other arts, taste of the mathematical sciences, specially Arithmetike and Geometry, without which it is not possible to attayn full knowledg in any art. Which may sufficiẽtly by gathered by Aristotle not õly in his bookesof demonstration (whiche can not be vnderstand without Geometry) but also in all his other workes. And before him Plato his maister wrote this sentence on his schole house dore.Αγεομέτρητοσ ὀυδὲισ ἐισΐτω.. Let no man entre here (saith he) without knowledg in Geometry. Wherfore moste mighty prince, as your most excellent Maiesty appeareth to be borne vnto most perfect felicity, not only by reasõ that God moued with the long prayers of this realme, did send your highnes as moste comfortable inheritour to the same, but also in that your Maiesty was borne in the time of such skilful schoolmaisters & learned techers, as your highnes doth not a little reioyse in, and profite by them in all kind of vertu & knowledg. Amõgst which is that heauẽly knowledg most worthely to be praised, wherbi the blindnes of errour & superstition is exiled, & good hope cõceiued that al the sedes & fruts therof, with all kindes of vice & iniquite, wherby vertu is hindered, & iustice defaced, shal be cleanextrirpedand rooted out of this realm, which hope shal increase more and more, if it may appear that learning be estemed & florish within this realm. And al be it the chief learnĩg be the diuine scriptures, which instruct the mind principally, & nexte therto the lawes politike, which most specially defẽd the right of goodes, yet is it not possible that those two can long be wel vsed, if that ayde want that gouerneth health and expelleth sicknes, which thing is done by Physik, & these require the help of the vij. liberall sciences, but of none more then of Arithmetik and Geometry, by which not only great thinges ar wrought touchĩg accõptes in al kinds, & in suruaiyng & measuring of lãdes, but also al arts depend partly of thẽ, & building which is most necessary can not be wtout them, which thing cõsidering, moued me to help to serue your maiesty in this point as wel as other wais, & to do what mai be in me, ytnot õly thei which studi prĩcipalli for lernĩg, mai haue furderãce bi mi poore help, butalso those whiche haue no tyme to trauaile for exacter knowlege, may haue some helpe to vnderstand in those Mathematicall artes, in whiche as I haue all readye set forth sumwhat of Arithmetike, so god willing I intend shortly to setforth a more exacter worke therof. And in the meane ceason for a taste of Geometry, I haue sette forthe this small introduction, desiring your grace not so muche to beholde the simplenes of the woorke, in comparison to your Maiesties excellencye,as to fauour the edition thereof, for the ayde of your humble subiectes, which shal thinke them selues more and more dayly bounden to your highnes, if when they shall perceaue your graces desyre to haue theym profited in all knowledge and vertue. And I for my poore ability considering your Maiesties studye for the increase of learning generally through all your highenes dominions, and namely in the vniuersities of Oxforde and Camebridge, as I haue an earnest good will as far as my simple seruice and small knowledg will suffice, to helpe toward the satisfiyng of your graces desire, so if I shall perceaue that my seruice may be to your maiesties contẽtacion, I wil not only put forth the other two books, whiche shoulde haue beene sette forth with these two, yf misfortune had not hindered it, but also I wil set forth other bookes of more exacter arte, bothe in the Latine tongue and also in the Englyshe, whereof parte bee all readye written, and newe instrumentes to theym deuised, and the residue shall bee eanded with all possible speede. I was boldened to dedicate this booke of Geometrye vnto your Maiestye, not so muche bycause it is the firste that euer was sette forthe in Englishe, and therefore for the noueltye a straunge presente, but for that I was perswaded, that suche a wyse prince doothe desire to haue a wise sorte of subiectes. For it is a kynges chiefe reioysinge and glory, if his subiectes be riche insubstaunce, and wytty in knowledge: and contraryewaies nothyng can bee more greuouse to a noble kyng, then that his realme should be other beggerly or full of ignoraunce: But as god hath geuen your grace a realme bothe riche in commodities and also full of wyttie men, so I truste by the readyng of wyttie artes (whiche be as the whette stones of witte) they muste needes increase more and more in wysedome, and peraduenture fynde some thynge towarde the ayde of their substaunce, whereby your grace shall haue newe occasion to reioyce, seyng your subiectes to increase in substance or wisdom, or in both. And thei again shal hauenew and newcauses to pray for yourmaiestie, perceiuyngso graciouse a mind towarde their benefite. And I truste (as I desire) that a great numbre of gentlemen, especially about the courte, whiche vnderstand not the latin tong, or els for the hardnesse of the mater could not away with other mens writyng, will fall in trade with this easie forme of teachyng in their vulgar tong, and so employe some of their tyme in honest studie, whiche were wont to bestowe most part of their time in triflyng pastime: Forvndoubtedlyiftheymean other your maiesties seruice, other their own wisdome, they will be content to employ some tyme aboute this honest and wittie exercise. For whose encouragemẽt to the intent they maie perceiue what shall be the vse of this science, I haue not onely written somewhat of the vse of Geometrie, but also I haue annexed to this boke the names and brefe argumentes of those other bokes whiche I will set forth hereafter, and that as shortly as it shall appeare vnto your maiestie by coniecture of their diligent vsyng of this first boke, that they wyll vse well the other bokes also. In the meane ceason, and at all times I wil be a continuall petitioner, that god may work in all english hartes an ernest mynde to all honest exercises, wherby thei may serue the better your maiestie andthe realm. And for your highnes I besech the most mercifull god, as he hath most fauourably sent you vnto vs, as our chefe comforter in earthe, so that he will increase your maiestie daiely in all vertue and honor with moste prosperouse successe, and augment in vs your most humble subiectes, true loue to godward, and iust obedience toward your highnes with all reuerence and subiection.
At London the .xxviij. daie of Ianuarie. M. D. L I.