## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 104

Dividendo , by division ; when there are four proportionals , and it is inferred , that the

Dividendo , by division ; when there are four proportionals , and it is inferred , that the

**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 . Page 124

If four magnitudes be proportionals , they are also proportionals by conversion : that is , the first is to its

If four magnitudes be proportionals , they are also proportionals by conversion : that is , the first is to its

**excess**above the second , as the third to its**excess**above the fourth . Let AB be to BE , as CD to DF : then BA shall be to ... Page 128

If the same hypothesis be made as in the proposition , the

If the same hypothesis be made as in the proposition , the

**excess**of the first and fifth shall be to the second , as the**excess**of the third and sixth to the fourth . The demonstration of this is the same with that of the proposition ... Page 162

... C. Make * the parallelogram KLMN equal to the

... C. Make * the parallelogram KLMN equal to the

**excess**of EF above C , and similar and similarly situated to D : then , since D is similar + to EF , therefore * also KM is similar to EF : let KL be the homologous side to EG , с # 26. Page 163

Let AB be the given straight line , and C the given rectilineal figure to which the parallelogram to be applied is required to be equal , and D the parallelogram to which the

Let AB be the given straight line , and C the given rectilineal figure to which the parallelogram to be applied is required to be equal , and D the parallelogram to which the

**excess**of the one to be applied above that upon the given ...### What people are saying - Write a review

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

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added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole