## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

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**excess**of the first above the second , is to the second , as the**excess**of the third above the fourth , is to the fourth . 17th Prop . book 5 . XVII . Convertendo , by conversion ; when there are four proportionals , and it * See Note ... Page 120

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**excess**above the fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is any number of magnitudes more than two , and as many others , so that they are proportionals when ... Page 142

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**excess**above the second , as the third to its**excess**above the fourth . Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by divi- sion ( 17. 5. ) , AE is to EB , as CF to FD , and by ... Page 148

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**excess**of the first and fifth shall be to the second , as the**excess**of the third and sixth to the fourth . The demon- stration of this is the same with that of the proposition , if divi- sion be used instead of composition . COR . 2 ... Page 184

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**excess**of EF above C , and similar and similarly situated to D ; but D is similar to EF , therefore ( 21. 6. ) also KM is similar to EF ; let KL * See Note : be the homologous side to EG , and LM , 184 BOOK VI . THE ELEMENTS OF EUCLID .### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore