The Elements of Euclid |
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Page 141
... adding the common part HK to both , GK is greater than HX ; wherefore also LN is greater than MP : and by taking away MN from both , LM is greater than NP : therefore , if GH be greater than KX , LM is greater than NP . In like manner ...
... adding the common part HK to both , GK is greater than HX ; wherefore also LN is greater than MP : and by taking away MN from both , LM is greater than NP : therefore , if GH be greater than KX , LM is greater than NP . In like manner ...
Page 143
... adding NM to both , LM is greater than NP : therefore , if GH be greater than KO , K LM is greater than NP . In like man- ner it may be shown , that if GH be equal to KO , LM is equal to NP ; and if less , less . And in the case in ...
... adding NM to both , LM is greater than NP : therefore , if GH be greater than KO , K LM is greater than NP . In like man- ner it may be shown , that if GH be equal to KO , LM is equal to NP ; and if less , less . And in the case in ...
Page 150
... added equal magnitudes , viz . to GB the two AG and F , and CH and E to HD ; AB and F together are greater than CD and E. Therefore , if four magnitudes , & c . Q. E. D. See Note . PROP . F. THEOR . RATIOS which are compounded of the ...
... added equal magnitudes , viz . to GB the two AG and F , and CH and E to HD ; AB and F together are greater than CD and E. Therefore , if four magnitudes , & c . Q. E. D. See Note . PROP . F. THEOR . RATIOS which are compounded of the ...
Page 187
... adding SR to each , the f 34. 1 . whole OB is equal to the whole XB : but XB is equals to TE , g 36. 1 . because the base AE is equal to the base EB ; wherefore also TE is equal to OB : add XS to each , then the whole TS is equal to the ...
... adding SR to each , the f 34. 1 . whole OB is equal to the whole XB : but XB is equals to TE , g 36. 1 . because the base AE is equal to the base EB ; wherefore also TE is equal to OB : add XS to each , then the whole TS is equal to the ...
Page 299
... added at the end of this definition in all the copies , but are now left out as not belonging to the definition , being only a corollary from it . Proclus demonstrates it by conceiving one of the parts into which the diameter divides ...
... added at the end of this definition in all the copies , but are now left out as not belonging to the definition , being only a corollary from it . Proclus demonstrates it by conceiving one of the parts into which the diameter divides ...
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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