The Elements of Euclid |
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Page vi
... given of compound ratio , and giving an absurd one in place of it in the 5th definition of the 6th book , which ... given , is put in its proper place among the definitions of the 5th book , by which the doctrine of compound ratios is ...
... given of compound ratio , and giving an absurd one in place of it in the 5th definition of the 6th book , which ... given , is put in its proper place among the definitions of the 5th book , by which the doctrine of compound ratios is ...
Page 175
... given straight line similar to one given , and so on . Which was to be done . : PROP . XIX . THEOR . 712 SIMILAR triangles are to one another in the du- plicate ratio of their homologous sides . Let ABC , DEF be similar triangles ...
... given straight line similar to one given , and so on . Which was to be done . : PROP . XIX . THEOR . 712 SIMILAR triangles are to one another in the du- plicate ratio of their homologous sides . Let ABC , DEF be similar triangles ...
Page 188
... given rec- tilineal C , exceeding by the parallelogram PO , which is simi- lar to D , because PO is similar to ELs . Which was to be done . PROP . XXX . PROB . TO cut a given straight line in extreme and mean ratio . Let AB be the given ...
... given rec- tilineal C , exceeding by the parallelogram PO , which is simi- lar to D , because PO is similar to ELs . Which was to be done . PROP . XXX . PROB . TO cut a given straight line in extreme and mean ratio . Let AB be the given ...
Page 189
... ratio in Ef . Which was to be done . Otherwise , Let AB be the given straight line ; it is required to cut it in extreme and mean ratio . f 3. def . 6 . Divide AB in the point C , so that the rectangle contained by AB , BC be equal to ...
... ratio in Ef . Which was to be done . Otherwise , Let AB be the given straight line ; it is required to cut it in extreme and mean ratio . f 3. def . 6 . Divide AB in the point C , so that the rectangle contained by AB , BC be equal to ...
Page 312
... given angle , though there neither is , nor can be any thing in the proposition relating to a given angle . PROP ... give a general " and summary idea of ratio to beginners , by premising " this metaphysical definition , to the more ...
... given angle , though there neither is , nor can be any thing in the proposition relating to a given angle . PROP ... give a general " and summary idea of ratio to beginners , by premising " this metaphysical definition , to the more ...
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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