The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 313
Viz. the First Six Books, Together with the Eleventh and Twelfth Euclid. PROP . I. PROBLEM . Three magnitudes , A , B , C , being given , to find a fourth such , that every three shall be greater than the remaining one . Let D be the ...
Viz. the First Six Books, Together with the Eleventh and Twelfth Euclid. PROP . I. PROBLEM . Three magnitudes , A , B , C , being given , to find a fourth such , that every three shall be greater than the remaining one . Let D be the ...
Page 337
... given , when a ratio of a given magnitude to a given magnitude which is the same I ratio with it can be found . have III . Rectilineal figures are said to be given in species , which each of their angles given , and the ratios of their ...
... given , when a ratio of a given magnitude to a given magnitude which is the same I ratio with it can be found . have III . Rectilineal figures are said to be given in species , which each of their angles given , and the ratios of their ...
Page 338
... given in magnitude , when the angles in them , and their bases , are given in magnitude . VIII . Segments of circles are said to be given in position and magnitude , when the angles in them are given in magnitude , and their bases are given ...
... given in magnitude , when the angles in them , and their bases , are given in magnitude . VIII . Segments of circles are said to be given in position and magnitude , when the angles in them are given in magnitude , and their bases are given ...
Page 339
... given magnitude have a given ratio to another magni- See N. tude , " and if unto the two magnitudes by which the " given ratio is exhibited , and the given magnitude , a " fourth proportional can be found , " the other magni- tude is ...
... given magnitude have a given ratio to another magni- See N. tude , " and if unto the two magnitudes by which the " given ratio is exhibited , and the given magnitude , a " fourth proportional can be found , " the other magni- tude is ...
Page 340
... given , because DF has been found which is equal to it . * 1 Def . * 1 Def 12 . 1 See N .. * 4 Dat . PROP . IV . If a given magnitude be taken from a given magnitude ; the remaining magnitude shall be given . A From the given magnitude AB , ...
... given , because DF has been found which is equal to it . * 1 Def . * 1 Def 12 . 1 See N .. * 4 Dat . PROP . IV . If a given magnitude be taken from a given magnitude ; the remaining magnitude shall be given . A From the given magnitude AB , ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore