The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 164
... given rectilineal figure C , exceeding by the parallelogram PO , which is similar to D , because PO is similar to EL . Which was to be done .. * PROP . XXX . PROB . To cut a given straight line in extreme and mean ratio . Let AB be the ...
... given rectilineal figure C , exceeding by the parallelogram PO , which is similar to D , because PO is similar to EL . Which was to be done .. * PROP . XXX . PROB . To cut a given straight line in extreme and mean ratio . Let AB be the ...
Page 280
... proportion of num- " bers to one another is defined , and treated of , yet " without giving any definition of the ratio of numbers ; " though such a definition was as necessary and useful " to be given in that book as in this : but ...
... proportion of num- " bers to one another is defined , and treated of , yet " without giving any definition of the ratio of numbers ; " though such a definition was as necessary and useful " to be given in that book as in this : but ...
Page 287
... given a more explicit demonstration than that which I found in the Elements . PROP . X. B. V. It was necessary to ... ratio than B to C : I say " that A is greater than B : for if it be not greater it is " either equal or less . But A cannot ...
... given a more explicit demonstration than that which I found in the Elements . PROP . X. B. V. It was necessary to ... ratio than B to C : I say " that A is greater than B : for if it be not greater it is " either equal or less . But A cannot ...
Page 288
... ratio of A to C be greater than the ratio of B to C ; that is , it should have been proved , that , in this case ... given the demonstration of the 10th proposition as we now have it instead of that which Eu- doxus or Euclid had given ...
... ratio of A to C be greater than the ratio of B to C ; that is , it should have been proved , that , in this case ... given the demonstration of the 10th proposition as we now have it instead of that which Eu- doxus or Euclid had given ...
Page 296
... proportion- als by reason of again neglecting permutation . On these accounts , a demonstration is given in Euclid's manner , like to that he makes use of in the 20th Prop . of this Book ; and it is extended to five - sided figures , by ...
... proportion- als by reason of again neglecting permutation . On these accounts , a demonstration is given in Euclid's manner , like to that he makes use of in the 20th Prop . of this Book ; and it is extended to five - sided figures , by ...
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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