The svrveyor in foure bookes / By Aaron Rathborne.

  • Aaron Rathborne
Date:
1616
Catalogue details

Licence: Public Domain Mark

Credit: The svrveyor in foure bookes / By Aaron Rathborne. Source: Wellcome Collection.

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    Lhe Surueyor. Parrt.2. THEOREME XLVIL | | Two right lines being drawne in an equilater Equiangle Pentagon,in Such fort asthey fubtend any two of the next immediate angles,thofe two lines by their interfections fhall diutde the one the other byan | extreame and meane proportion: and the greater fegments of either of them [hall be equall to the fide of the Pentagon, Et A.B. and GsD. be two right lines,-drawne in the Equilater E- quiangled Pentagon, A. D. B. E.G. and let the line A. B. fubtend the angle A.D. B. and the line C. D. the angle G. A. D. being two of the next imme- diateangles. I fay then,that thofe two lines, by their interfection in the point F. fhall diuide the one the other by an extreame and meane proportion. And the greater fegments of either of them, as the fegments F.B. and F. C. fhall be either of them equall to the fideof the Pentagon A.D.B.E.C. Paos.20.21. 48.62.63. 119.120. THeoremMe XLVIIL Like Triangles are one to the other in donble proportion that the fides of : | like proportion are, Et A.B.G.and D.E. F. be 4 [T's like Triangles,andlee A . theangle A, of theonebe |S equall to the angle D: of the o- ther ; the angle B. of the one, to the angle E. of the other; and the angle C. of the onetothean- gle F. of the other ; and as the fide A.B. is to the fideB. C. fo let the fide D. E. be to the fide E. F. foare B. C.and EF. fides of like proportion. Now I fay, that the proportion of the Tri- i angle A. B. C. vnto the Trian- Bt! gle D.E.F. is double the proportion of the fide B. C. to the fideE.F, | tk PROB. 45. By THEo= |
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