Euclides Elements of geometry: the first VI books: in a compendious form contracted and demonstrated / By Thomas Rudd ... Whereunto is added the mathematicall preface of John Dee.

  • Euclid.
Date:
1651
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Licence: Public Domain Mark

Credit: Euclides Elements of geometry: the first VI books: in a compendious form contracted and demonstrated / By Thomas Rudd ... Whereunto is added the mathematicall preface of John Dee. Source: Wellcome Collection.

    393/400 (page 259)
    andF, it followeth (by the 14 of the fixt book) that the lines are to their parts reciprocally proportioned according to the propofition, and (by the fame 36 of the fixt book) is the fquareof the line P B,equall to the right angle fi¬ gure made of P Rand P G, or of P H and P F, it follow¬ eth then (by the 17 of thefixt book) that the line P B is the mean proportionall between P R and P G, or P H and P F. Propofition 6. If two right lines doe fiand between two parallel lines which are cut through with a third parallel line, that is done in equail proportion. Conftru&ion. The two {landing lines are AB and C D, they Hand between the two parallel lines A C and B D, and are cut through with another parallel line H F in the points H and F, that cutting doth happen in cquall proportion, namely,as AH to HB, fo C F to F D. . > Demonftration. Let the line C Bbe drawn, cutting H F in I, forafmuch as (by the fecondof the fixt book) A H is to Η B, as CI is to I B, and C F to F D, as the fame C l is to I B,it follow¬ eth (by the ii of thefift book) that the propofition is true. FINIS.