The Elements of Euclid |
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Page vi
... given ; and by taking out of this book , besides other things , the good ... magnitude . ” Now this proposition is a theorem , not a definition ; because ... magnitude , and yet be unequal to one another ; as shall be made evident in the ...
... given ; and by taking out of this book , besides other things , the good ... magnitude . ” Now this proposition is a theorem , not a definition ; because ... magnitude , and yet be unequal to one another ; as shall be made evident in the ...
Page 315
... given the method of doing . For this rea- son , we have changed the construction to one , which , without doubt , is Euclid's , in which no- thing is required but to add a magnitude to itself a certain number of times ; and this is to ...
... given the method of doing . For this rea- son , we have changed the construction to one , which , without doubt , is Euclid's , in which no- thing is required but to add a magnitude to itself a certain number of times ; and this is to ...
Page 320
... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude ...
... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude ...
Page 338
... given space : or , which is the same thing , having given AB the sum of the sides of a rectangle , and the magnitude of it being likewise given , to find its sides . And the fourth problem is the same with this , To find the point N in the ...
... given space : or , which is the same thing , having given AB the sum of the sides of a rectangle , and the magnitude of it being likewise given , to find its sides . And the fourth problem is the same with this , To find the point N in the ...
Page 341
... magnitude , that are neither similar nor equal , shall be demonstrated after ... Magnitudes that wholly coincide , are equal " to one another ; " or from prop ... given no definition of equal figures , and it is certain he did not give ...
... magnitude , that are neither similar nor equal , shall be demonstrated after ... Magnitudes that wholly coincide , are equal " to one another ; " or from prop ... given no definition of equal figures , and it is certain he did not give ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore