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

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Page 44

Q. E. D. From this proposition it is manifest , that the

Q. E. D. From this proposition it is manifest , that the

**difference**of the squares of two unequal lines , AC , CD , is equal to the rectangle contained by their sum and dif+1 Ax . + 2 Ax . ference . PROP . VI . THEOR . Page 99

... the circumference ABC , being the third part of the whole , contains five ; and the circumference AB , which is the fifth part of the whole , contains three ; therefore BC , their

... the circumference ABC , being the third part of the whole , contains five ; and the circumference AB , which is the fifth part of the whole , contains three ; therefore BC , their

**difference**, contains two of the same parts : bisect ... Page 268

... that he may supply the omission he blames Euclid for , which determination is , that any of the three straight lines must be less than the sum , but greater than the

... that he may supply the omission he blames Euclid for , which determination is , that any of the three straight lines must be less than the sum , but greater than the

**difference**of the other two : from this he shews the circles must ... Page 283

He says , he would not leave it out , because it was fine , and might sharpen one's genius to invent others like it : whereas there is not the least

He says , he would not leave it out , because it was fine , and might sharpen one's genius to invent others like it : whereas there is not the least

**difference**between the two demonstrations , except a single word in the construction ... Page 298

... merely upon ac“ count of two ratios being interposed betwixt the s extremes , that are equal to one another : so that there " is no

... merely upon ac“ count of two ratios being interposed betwixt the s extremes , that are equal to one another : so that there " is no

**difference**betwixt the compounding of ratios , " and the duplication or triplication of them which ...### 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 |

### Common terms and phrases

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