Part 12

And herof commeth that seconnde thing wherin al agree [that seconnde . thing] if they can with their wysedome ouercome all vyces. Of the firste of those three sortes [_text reads "... their rwysedome ... / ... th ee sortes ..." on consecutive lines. The extraneous "r" is directly above the missing or invisible "r"_] #akroamatikoi#. [_final . missing_] was he estemed for his wisdom. [_final . missing_] wisedom is better then pretious stones . yea [_punctuation unchanged_] your Maiesties excellencye, [excellencye,,] if his subiectes be riche in substaunce, [sub staunce] new and new causes to pray for your maiestie, perceiuyng [maiestie,perceiuyng] can be ignorant thereof, in so much that [thereof. in] those thynges are done by negromancy. [_spelling unchanged_] thogh it be but smal, and thefore not notable. [_final . missing_] but boweth any waye, such are called [waye. such] not call it one croked lyne, but rather [cr oked] Now to geue you example of triangles, [triangles,,] a portion of a globe as the figur marked w^t A. [_final . missing_] as is the figure G. other ij. sharp and one blunt these examples .M. N, and O. where M. hath a right angle, N, a blunte angle [.M.N, and O where ... N, A, blunte] as in this example because A.B, is drawen in length [A,B,] the angle C, is called an vtter angle. [_final . missing_] _diamondlike_, whose figur is noted with T. [_final . missing_] and partlye vnequall, as in B, and they [in, B and] as in this figure is some what expressed. [_final . missing_] then draw a line from B, to F, & so I haue mine intent. [_final . missing_] then open I the compasse as wyde as A.C, [A,C,] F, this space betwene D. and F. [betwene D and F.] crosse that other first line in .ij. places. [_final . missing_] The arch to be diuided ys A.D.C, the corde is A.B.C, [A,B.C,] and ther set a mark. Then take a long line [mark Then] a parallel must be drawen howe you shall doo it. [doo it,] equal to A.B, as for example D.F. [D,F.] accordyng to the fifth conclusion [accordyngt o] (accordyng as the .viij. conclusion teacheth) [_comma for close parenthesis_] it hath one angle (that is B.A.E.) like to D [_close parenthesis missing_] therefore I wyl by example sette forth [ther efore] thenne drawe I a line also from N. vnto C. [vnto C] is equall vnto A.B, and so is K.L. [K.L,] you mai se by C. and D, for ij. sides [by C and D,] accordyng to the lengthe lo the peece that remaineth [_error for "of the"?_] [th e peece] this line A.B, (w^{ch} was assigned vnto me) [A,B,] & thus haue you attained y^e vse of this conclusion. [_final . missing_] Make in a table the like draught [A table] vsing it as it wer a croked ruler. [_final . missing_] the lines of diuision A.D, B.E [A. D. B. E] whose two sides A.C. and B.C. are diuided [B,C.] enclose those iij prickes. that centre as you se is D [prickes that centre . as] as you se B.A.D, and B.C.E. [B.C,E.] at this tyme wyll shewe you [she,we] as youre selfe mai easily gesse. [_final . missing_] A.C. and B.D. are the two diameters [A.C. and B D.] A.B.C.D. is the quadrate appointed [A,B.C.D.] quadrate from angle to angle, as you se A.C. & B D. [A.C. & B D.] A.B.C. is the circle, whiche I haue deuided [A,B.C.] And from eche pricke ij. lines drawen [line sdrawen] I would make a circle. Therfore I drawe [circle, Therfore] of equall sides and equall angles. [angles,] perceaue by the xxxvij. xxxviij. xxxix. and xl. conclusions [xxxviij xxxix.] that be nighest [that be . nighest] learne the demonstrations by harte, (as somme [_missing open parenthesis_] sundrye woorkes partely ended, and partely to bee ended [And] As for example A--------B. A. being the one pricke [A being] that corner which is greatter then a right angle [_s in "is" invisible_] firste these two right lines A.B. and A.C. [A B. and A.C.] ij. quantities, as A. and B, be equal to an other [as A and B,] in an other place. In the mean season [in] drawen forthe vnto D. and E. [vnto D and E.] [The thirde Theoreme.] Example. [_final . missing_] and yet the ij. lesser sides togither ar greater then it. [_text has "... yet thr ... ar greate" at consecutive line-ends_] the angle C. (whiche are the ij. angles contayned [_missing open parenthesis_] M.N. equall also to H.L. [H,L.] therefore are A.C. and B.D. bothe equall [A,C.] A.D.E, and D.E.B, which (as the xxvij. [_missing open parenthesis_] _The xxxi. theoreme._ [xxxi, theoreme.] there is made a triangle B.C.G, and a lykeiamme [B.C G,] fyll vp the sydes of the .ij. fyrste square lykeiammes [.ij fyrste] equall to the .ij. squares of both the other sides. [_final . missing_] The ij. lines proposed ar A.B. and C.D [A B. and C.D] for the square D.E.F.G. is equal to the two other partial squares of D.H.K.G and H.E.F.K, [D,E.F.G. ... D.H.K G] _The xxxvij. Theoreme._ [xxxvij Theoreme.] the square that is made of the whole line [_first t in "that" invisible_] (which is equall with D.G.) [D,G.] Lette the diuided line bee A.B, and parted in C [A,B,] the square of the whole lyne A.B, [A,B,] as herafter I will declare in conuenient place. [_final . missing_] two lesser squares beyng taken away, [_close parenthesis for comma_] the great square, and that is G.F.M.H. [G,F.M.H.] two vnequall partes as happeneth. The long square [the] _The .xlvi. Theoreme._ [The.xlvi.] _The xlvij. Theoreme._ [xlvij Theoreme.] and doo not passe by the centre [passeby] For as you may easily iudge, A.C. hath one portion [A C.] if they be equally distaunt from one halfe of the diameter [_second l in "equally" invisible_] then it, and beynge farther of [it. and] the second circle is B.C.D.E, and they crosse [B.C.D,E,] The second circle is D.B.C, and his centre is H [D,B.C,] that is farther from the centre. The fourth [centre, The] twise so great as the other angle on the circumference. [_final . missing_] The lesser is D.E.C, and the geater is D.A.B.C. [D.F.C,] therefore are they both equall. [_final . missing_] What is ment by like cantles you haue heard before [mentby] by the equalitie of the righte lines, so dothe this Theoreme [so do the this] Also it is meet to note y^t al angles that be made [y^{t}al] whiche maketh two cantles of the whole circle. [circle,] which is made of a line A.B, and the line A.D, [A,B,] I saie accordyng to the Theoreme, that the .ij. angles [.ij angles] so that the angle B.D.F, is equall to the angle B.A.D [B D.F,] make their portions somewhat toward an equalitie. [_final . missing_] doth crosse thother line B.D, in y^e point E. [B D,] whiche was A. Nowe concernyng the meanyng [No we]

End of Project Gutenberg's The Path-Way to Knowledg, by Robert Record