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A10541 The pathvvay to knowledg containing the first principles of geometrie, as they may moste aptly be applied vnto practise, bothe for vse of instrumentes geometricall, and astronomicall and also for proiection of plattes in euerye kinde, and therefore much necessary for all sortes of men. Record, Robert, 1510?-1558. 1551 (1551) STC 20812; ESTC S115664 86,278 175

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them whiche is doone to this intent that yf any manne lyst to learne the demonstrations by harte as somme learned men haue iudged beste to doo those same men should finde the Linearye exaumples to serue for this purpose and to wante no thyng needefull to the iuste proofe whereby this booke maye bee wel approued to be more complete then many men wolde suppose it And thus for this tyme I wyll make an ende without any larger declaration of the commoditees of this arte or any farther answeryng to that may bee obiected agaynst my handelyng of it wyllyng them that myslike it not to medle with it and vnto those that will not disdaine the studie of it I promise all suche aide as I shall be able to shewe for their farther procedyng bothe in the same and in all other commoditees that thereof maie ensue And for their incouragement I haue here annexed the names and brefe argumentes of suche bookes as I intende God willyng shortly to sette forth if I shall perceaue that my paynes maie profyte other as my desyre is The brefe argumentes of suche bokes as ar appoynted shortly to be set forth by the author herof THE seconde part of Arithmetike teachyng the workyng by fractions with extraction of rootes both square and cubike And declaryng the rule of allegation with sundrye pleasaunt exaumples in metalles and other thynges Also the rule of false position with dyuers examples not onely vulgar but some appertaynyng to the rule of Algeber applied vnto quantitees partly rationall and partly surde THE arte of Measuryng by the quadrate geometricall and the disorders committed in vsyng the same not only reueled but reformed also as muche as to the instrument pertayneth by the deuise of a newe quadrate newely inuented by the author hereof THE arte of measuryng by the astronomers staffe and by the astronomers ryng and the form of makyng them both THE arte of makyng of Dials bothe for the daie and the nyght with certayn new formes of fixed dialles for the moon and other for the sterres whiche may bee sette in glasse windowes to serue by daie and by night And howe you may by those dialles knowe in what degree of the Zodiake not only the sonne but also the moone is And how many howrs old she is And also by the same dial to know whether any eclipse shall be that moneth of the sonne or of the moone The makyng and vse of an instrument wherby you maye not onely measure the distance at ones of all places that you can see togyther howe muche eche one is from you and euery one from other but also therby to drawe the plotte of any countreie that you shall come in as iustely as maie be by mannes diligence and labour THE vse bothe of the Globe and the Sphere and therin also of the arte of Nauigation and what instrumentes serue beste thervnto and of the trew latitude and longitude of regions and townes Euclides woorkes in foure partes with diuers demonstrations Arithmeticall and Geometricall or Linearie The fyrst parte of platte formes The second of numbres and quantitees surde or irrationall The third of bodies and solide formes The fourthe of perspectiue and other thynges thereto annexed BESIDE these I haue other sundrye woorkes partely ended And partely to bee ended Of the peregrination of man and the originall of al nations The state of tymes and mutations of reasmes The image of a perfect common welth with diuers other woorkes in naturall sciences Of the wonderfull workes and effectes in beastes plantes and minerals of whiche at this tyme I will omitte the argumentes beecause thei doo appertaine littell to this arte and handle other matters in an other sorte To haue or leaue Nowe maie you chuse No paine to please Will I refuse The Theoremes of Geometry before WHICHE ARE SET FORTHE certaine grauntable requestes whiche serue for demonstrations Mathematicall That frō any pricke to one other there may be drawen a right line AS for example A being the one pricke and B. the other you maye drawe betwene them from the one to the other that is to say frome A. vnto B and from B. to A. That any right line of measurable length may be drawen forth longer and straight Example of A. B which as it is a line of measurable lengthe so may it be drawen forth farther as for exaumple vnto C and that in true streightenes without crokinge That vpon any centre there may be made a circle of anye quātitee that a man wyll Let the centre be set to be A what shal hinder a man to drawe a circle aboute it of what quantitee that he lusteth as you se the forme here other bygger or lesse as it shall lyke him to doo That all right angles be equall eche to other Set for an example A. and B of which two though A. seme the greatter angle to some men of small experience it happeneth only bicause that the lines aboute A are longer thē the lines about B as you may proue by drawing them longer for so shal B. seme the greater angle ▪ yf you make his lines longer then the lines that make the angle A. And to proue it by demonstration I say thus If any ij right corners be not equal then one right corner is greater then an other but that corner which is greatter then a right angle is a blunt corner by his definition so must one corner be both a right corner and a blunt corner also which is not possible And againe the lesser right corner must be a sharpe corner by his definition bicause it is lesse then a right angle which thing is impossible Therefore I conclude that all right angles be equall Yf one right line do crosse two other right lines and make ij inner corners of one side lesser thē ij righte corners it is certaine that if those two lines be drawen forth right on that side that the sharpe inner corners be they wil at lēgth mete togither and crosse on an other The ij lines beinge as A. B. and C. D and the third line crossing them as dooth heere E. F making ij inner cornes as ar G.H. lesser then two right corners fithech of them is lesse then a right corner as your eyes maye iudge then say I if those ij lines A.B. and C.D. be drawen in lengthe on that side that G. and H. are the will at length meet and crosse one an other Two right lines make no platte forme A platte forme as you harde before hath bothe length and hredthe and is inclosed with lines as with his boundes but ij right lines cannot inclose al the bondes of any platte forme Take for an example firste these two right lines A B. and A. C whiche meete togither in A but yet cannot be called a platte forme bicause there is no bond from B. to C but if you will drawe a line betwene them twoo that is frome B. to C then will it be a platte forme that