Linguistic DNA - Concept Modelling Demonstrator

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	erect_v	line_n	plain_a	2,288	5	10.8979	5	true

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
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

with my compas I take the length of A. B. and set the one foote of my compas in C and draw an arch line with the other foote Likewaies I take the leÌ„gth of E. F and set one foote in D and with the other foote I make an arch line crosse the other arche and the pricke of their metyng whiche is G. shall be the thirde corner of the triangle for in all suche kyndes of woorkynge to make a tryangle if you haue one line drawen there remayneth nothyng els but to fynde where the pitche of the thirde corner shall bee for two of them must needes be at the two candes of the lyne that is drawen THE XIII CONCLVSION If you haue a line appointed and a pointe in it limited howe you maye make on it a righte lined angle equall to an other right lined angle all ready assigned Fyrste draw a line against the corner assigned and so is it a triangle then take heede to the line and the pointe in it assigned and consider if that line from the pricke to this end bee as long as any of the sides that make the triangle assigned and if it bee longe inoughe then prick out there the length of one of the lines and then woorke with the other two lines accordinge to the laste conclusion makynge a triangle of thre like lynes to that assigned triangle If it bee not longe inoughe thenne lengthen it fyrste and afterwarde doo as I haue sayde beefore Example Lette the angle appoynted bee A. B. C and the corner assigned B. Farthermore let the lymited line bee D. G and the pricke assigned D. Fyrste therefore by drawinge the line A. C I make the triangle A.B.C. Then consideringe that D. G is longer thanne A. B you shall cut out a line froÌ„ D. toward G equâ—l to A. B as for exaÌ„ple D F. TheÌ„ measure oute the other ij lines and worke with theÌ„ according as the conclusion with the fyrste also and the second teacheth yow and then haue you done THE XIIII CONCLVSION To make a square quadrate of any righte lyne appoincted First make a plumbe line vnto your line appointed whiche shall light at one of the endes of it accordyng to the fifth conclusion and let it be of like length as your first line is then opeÌ„ your compasse to the iuste length of one of them and sette one foote of the compasse in the ende of the one line and with the other foote draw an arche line there as you thinke that the fowerth corner shall be after that set the one foote of the same compasse vnsturred in the cande of the other line and drawe an other arche line crosse the first arche line and the poincte that they do crosse in is the pricke of the fourth corner of the square quadrate which you seke for therfore draw a line from that pricke to the eande of eche line and you shall therby haue made a square quadrate Example A. B. is the line proposed of whiche I shall make a square quadrate therefore firste I make a pluÌ„be line vnto it whiche shall lighte in A and that pluÌ„b line is A. B then open I my compasse as wide as the length of A. B or B. C for they must be bothe equall and I set the one foote of th end in C and with the other I make an arche line nigh vnto D afterward I set the compas again with one foote in B A and with the other foote I make an arche line crosse the first arche line in D and from the prick of their crossyng I draw .ij. lines one to B A and an other to C and so haue I made the square quadrate that I entended THE XV. CONCLVSION To make a likeiaÌ„me equall to a triangle appointed and that in a right lined aÌ„gle limited First from one of the angles of the triangle you shall drawe a gemowe line whiche shall be a parallele to that syde of the triangle on whiche you will make that likeiamme Then on one end of the side of the triangle whiche lieth against the gemowe lyne you shall draw forth a line vnto the gemow line so that one angle that commeth of those .ij. lines be like to the angle whiche is limited vnto you Then shall you deuide into ij equall partes that side of the triangle whiche beareth that line and from the pricke of that deuision you shall raise an other line parallele to that former line and continewe it vnto the first gemowe line and theÌ„ of those .ij. last gemowe lynes and the first gemowe line with the halfe side of the triangle is made a lykeiamme equall to the triangle appointed and hath an angle lyke to an angle limited accordyng to the conclusion Example B. C. G is the triangle appoincted vnto whiche I muste make an equall likeiamme And D is the angle that the likeiamme must haue Therfore first entendyng to erecte the likeiaÌ„me on the one side that the ground line of the triangle whiche is B. G. I do draw a gemow line by C and make it parallele to the ground line B. G and that new gemow line is A. H. Then do I raise a line from B. vnto the gemowe line whiche line is A. B and make an angle equall to D that is the appointed angle accordyng as the .viij. coÌ„clusion teacheth and that angle is B. A. E. Then to procede I doo parte in the middle the said grouÌ„d line B. G in the prick F froÌ„ which prick I draw to the first gemowe line A. H. an other line that is parallale to A. B and that line is E. F. Now saie I that the likeiaÌ„me B. A. E. F is equall to the triangle B. C. G. And also that it hath one angle that is B. A. E. like to D. the angle that was limitted And so haue I mine intent The prose of the equalnes of those two figures doeth depend of the .xli. proposition of Euclides first boke and is the .xxxi. proposition of this second boke of Theoremis whiche saieth that whan a tryangle and a likeiamme be made betwene .ij. selfe same gemow lines and haue their ground line of one length then is the likeiamme double to the triangle wherof it foloweth that if .ij. suche figures so drawen differ in their ground line onely so that the ground line of the likeiamme be but halfe the ground line of the triangle then be those .ij. figures equall as you shall more at large perceiue by the boke of Theoremis in the .xxxi. theoreme THE XVI CONCLVSION To make a likeiamme equall to a triangle appoincted accordyng to an angle limitted and on a line also assigned In the last conclusion the sides of your likeiamme wer left to your libertie though you had an angle appoincted Nowe in this conclusion you are somwhat more restrained of libertie sith the line is limitted which must be the side of the likeiaÌ„me Therfore thus shall you procede Firste accordyng to the laste conclusion make a likeiamme

is to say a triangle but then are there iij. lines and not only ij Likewise may you say of D.E. and F. G whiche doo make a platte forme nother yet can they make any without helpe of two lines more whereof the one must be drawen from D. to F and the other frome E. to G and then will it be a longe square So then of two right lines can bee made no platte forme But of ij croked lines be made a platte forme as you se in the eye form And also of one right line one croked line maye a platte fourme bee made as the semicircle F. doothesette forth Certayn common sentences manifest to sence and acknowledged of all men The firste common sentence What so euer things be equal to one other thinge those same bee equall betwene them selues Examples therof you may take both in greatnes and also in numbre First though it pertaine not proprely to geometry but to helpe the vnderstandinge of the rules whiche may bee wrought by bothe artes thus may you perceaue If the summe of monnye in my purse and the mony in your purse be equall eche of them to the mony that any other man hathe then must needes your mony and mine be equall togyther Likewise if anye ij quantities as A and B be equal to an other as vnto C then muste nedes A. and B. be equall eche to other as A. equall to B and B. equall to A whiche thinge the better to peceaue tourne these quantities into numbre so shall A. and B. make fixteene and C. as many As you may perceaue by multipliyng the numbre of their sides togither The seconde common sentence And if you adde equall portions to thinges that be equall what so amounteth of them shall be equall Example Yf you and I haue like summes of mony and then receaue eche of vs like summes more then our summes wil be like styll Also if A. and B. as in the former example bee equall then by adding an equal portion to them both as to ech of them the quarter of A. that is foure they will be equall still The thirde common sentence And if you abate euen portions from things that are equal those partes that remain shall be equall also This you may perceaue by the laste example For that that was added there is subtracted heere and so the one doothe approue the other The fourth common sentence If you abate equalle partes from vnequal thinges the remainers shall be vnequall As bicause that a hundreth and eight and forty be vnequal if I take tenne from them both there will remaine nynetye and eight and thirty which are also vnequall and likewise in quantities it is to be iudged The fifte common sentence when euen portions are added to vnequalle thinges those that amounte shal be vnequall So if you adde twenty to fifty and lyke ways to nynty you shall make seuenty and a hundred and ten whiche are no lesse vnequall than were fifty and nynty The syxt common sentence If two thinges be double to any other those same two thinges are equal togither Bicause A. and B. are eche of them double to C therefore must A. and B. nedes be equall togither For as v. times viij maketh xl which is double to iiij times v that is xx so iiij times x likewise is double to xx for it maketh fortie and therefore muste neades be equall to forty The seuenth common sentence If any two thinges be the halfes of one other thing than are thei .ij. equall togither So are D. and C. in the laste example equal togyther bicause they are eche of them the halfe of A. other of B as their numbre declareth The eyght common sentence If any one quantitee be laide on an other and thei agree so that the one excedeth not the other then are they equall togither As if this figure A. B. C be layed on that other D. E. F so that A. be layed to D B. to E and C. to F you shall see them agre in sides exactlye and the one not to excede the other for the line A.B. is equall to D. E and the third lyne C. A is equal to F. D so that euery side in the one is equall to some one side of the other wherfore it is playne that the two triangles are equall togither The nynth common sentence Euery whole thing is greater than any of his partes This sentence nedeth none example For the thyng is more playner then any declaration yet considering that other commen sentence that foloweth nexte that The tenthe common sentence Euery whole thinge is equall to all his partes taken togither It shall be mete to expresse both with one example for of thys last seÌ„tence many meÌ„ at the first hearing do make a doubt Therfore as in this example of the circle deuided into suÌ„dry partes it doeth appere that no parte can be so great as the whole circle accordyng to the meanyng of the eight sentence so yet it is certain that all those eight partes together be equall vnto the whole circle And this is the meanyng of that common sentence whiche many vse and fewe do rightly vnderstand that is that All the partes of any thing are nothing els but the whole And contrary waies The whole is nothing els but all his partes taken togither whiche saiynges some haue vnderstand to meane thus that all the partes are of the same kind that the whole thyng is but that that meanyng is false it doth plainly appere by this figure A. B whose partes A. and B are triangles and the whole figure is a square and so are they not of one kind But and if they applie it to the matter or substance of thinges as some do then is it moste false for euery compound thyng is made of partes of diuerse matter and substance Take for example a man a house a boke and all other compound thinges Some vnderstand it thus that the partes all together can make none other forme but that that the whole doth shewe whiche is also false for I maie make fiue hundred diuerse figures of the partes of some one figure as you shall better perceiue in the third boke And in the meane seasoÌ„ take for an exaÌ„ple this square figure folowing A. B. C. D which is deuided but into two parts and yet as youse I haue made fiue figures more beside the firste with onely diuerse ioynyng of those two partes But of this shall I speake more largely in an other place in the mean season content your self with these principles whiche are certain of the chiefe groundes wheron all demonstrations mathematical are fourmed of which though the moste parte seeme so plaine that no childe doth doubte of them thinke not therfore that the art vnto whiche they serue is simple other childishe but rather consider howe certayne the profes of that arte is that hath for his grouÌ„des soche playne truthes as I may say suche vndowbtfull and

Selected quad for the lemma: ground_n

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