The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 313
... given in that book , as in this : but in " deed there is scarce any need of ... species of compound ratio . But Theon has made it the 5th def . of book 6 ... given , but they retain also Theon's , which they ought to have left out of the ...
... given in that book , as in this : but in " deed there is scarce any need of ... species of compound ratio . But Theon has made it the 5th def . of book 6 ... given , but they retain also Theon's , which they ought to have left out of the ...
Página 367
... given in magnitude , when equals to them can be found . II . A ratio is said to be given , when a ratio of a given ... species , which have each of their angles given , and the ratios of their sides given . IV . Points , lines , and ...
... given in magnitude , when equals to them can be found . II . A ratio is said to be given , when a ratio of a given ... species , which have each of their angles given , and the ratios of their sides given . IV . Points , lines , and ...
Página 396
... given in species . Let each of the sides of the triangle ABC be given in mag- nitude , the triangle ABC is given in species . Make a triangle a DEF , the sides of which are equal , each to each , to the given straight lines AB , BC , CA ...
... given in species . Let each of the sides of the triangle ABC be given in mag- nitude , the triangle ABC is given in species . Make a triangle a DEF , the sides of which are equal , each to each , to the given straight lines AB , BC , CA ...
Página 397
... given : and the points D , E are given ; therefore each of the straight lines 他 DE , EF , FD is given in magnitude : wherefore the triangle c 29. dat . c DEF is given in species d ; and it is similar to the triangle d 42 dat . ABC ...
... given : and the points D , E are given ; therefore each of the straight lines 他 DE , EF , FD is given in magnitude : wherefore the triangle c 29. dat . c DEF is given in species d ; and it is similar to the triangle d 42 dat . ABC ...
Página 398
... given in species . Let the sides of the triangle ABC have given ratios to one another , the triangle ABC is given in species . c A B D E F Take a straight line D given in magnitude ; and because the ratio of AB to BC is given , make the ...
... given in species . Let the sides of the triangle ABC have given ratios to one another , the triangle ABC is given in species . c A B D E F Take a straight line D given in magnitude ; and because the ratio of AB to BC is given , make the ...
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Términos y frases comunes
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