The Elements of Euclid |
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Page vi
... magnitude . ” Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and , there- fore , though this were a true proposition , it ought to have been ...
... magnitude . ” Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and , there- fore , though this were a true proposition , it ought to have been ...
Page vii
Euclid Robert Simson. plane angles of the same number and magnitude , placed in the same order ; but neither is this universally true , except in the case in which the solid angles are contained by no more than three plane anglesnor of ...
Euclid Robert Simson. plane angles of the same number and magnitude , placed in the same order ; but neither is this universally true , except in the case in which the solid angles are contained by no more than three plane anglesnor of ...
Page 119
... magnitude is said to be a part of a greater mag- nitude , when the less measures the greater , that is , when ' the less is contained a certain number of times exactly in the greater . ' ་ II . A greater magnitudé is said to be a ...
... magnitude is said to be a part of a greater mag- nitude , when the less measures the greater , that is , when ' the less is contained a certain number of times exactly in the greater . ' ་ II . A greater magnitudé is said to be a ...
Page 120
... Magnitudes which have the same ratio are called propor- tionals . N. B. When four magnitudes are proportionals , it ... magnitude . For example , if A , B , C , D be four magnitudes of the same kind , the first A is said to have to the ...
... Magnitudes which have the same ratio are called propor- tionals . N. B. When four magnitudes are proportionals , it ... magnitude . For example , if A , B , C , D be four magnitudes of the same kind , the first A is said to have to the ...
Page 122
... magnitudes are taken two and two . XIX . i Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank , as the first to the second of the other rank and as the se- cond ...
... magnitudes are taken two and two . XIX . i Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank , as the first to the second of the other rank and as the se- cond ...
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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