The Elements of Euclid |
From inside the book
Results 6-10 of 60
Page 139
... proportionals when taken alternately . Let the four magnitudes A , B , C , D be proportionals , viz . as A to B , so C to D : they shall also be probortionals when taken alternately ; that is , A is to C , as B to D. Take of A and B any ...
... proportionals when taken alternately . Let the four magnitudes A , B , C , D be proportionals , viz . as A to B , so C to D : they shall also be probortionals when taken alternately ; that is , A is to C , as B to D. Take of A and B any ...
Page 140
... proportionals , See Note . they shall also be proportionals when taken separately ; that is , if two magnitudes together have to one of them the same ratio which two others have to one of these , the remaining one of the first two shall ...
... proportionals , See Note . they shall also be proportionals when taken separately ; that is , if two magnitudes together have to one of them the same ratio which two others have to one of these , the remaining one of the first two shall ...
Page 141
... proportionals , See Note . they shall also be proportionals when taken jointly , that is , if the first be to the second , as the third to the fourth , the first and second together shall be to the second , as the third and fourth ...
... proportionals , See Note . they shall also be proportionals when taken jointly , that is , if the first be to the second , as the third to the fourth , the first and second together shall be to the second , as the third and fourth ...
Page 144
... proportionals , they are also proportionais b . when taken , separately ; there- fore , as BE is to DF , so is EA to ... proportionals , they are also proportionals by conversion , that is , the first is to its excess above the second ...
... proportionals , they are also proportionais b . when taken , separately ; there- fore , as BE is to DF , so is EA to ... proportionals , they are also proportionals by conversion , that is , the first is to its excess above the second ...
Page 149
... proportionals , they shall likewise be proportionals when taken . jointly b : as , therefore , AC is to GB , so is B- E- H DH to HE : but as GB to C , so is HE to F. Therefore , ex æqualia , as AG is to C , so is DH to F. Wherefore , if ...
... proportionals , they shall likewise be proportionals when taken . jointly b : as , therefore , AC is to GB , so is B- E- H DH to HE : but as GB to C , so is HE to F. Therefore , ex æqualia , as AG is to C , so is DH to F. Wherefore , if ...
Other editions - View all
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