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

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Page 46

( If a straight line be divided into any two parts , four times the

( If a straight line be divided into any two parts , four times the

**rectangle**contained by the whole line , and one of the parts , together with the square of the other part , is equal to the square of the straight line which is made up ... Page 47

the

the

**rectangle**AB , BC , is equal + to the gnomon AOH : + 1 Ax . to each of these add XH ; which is equal * to the square * Cor . 4. 2 • of AC ; therefore four times the**rectangle**AB , BC , to- and 34 , 1 , ' gether with the square of AC ... Page 50

To divide a given straight line into two parts , so that the

To divide a given straight line into two parts , so that the

**rectangle**contained by the whole , and one of the parts , shall be equal to the square of the other part . Let AB be the given straight line ; it is required to divide it into ... Page 51

4.2 . ť 2 Axo 1 duced , the square of the side subtending the obtuse angle , is greater than the squares of the sides containing the obtuse angle , by twice the

4.2 . ť 2 Axo 1 duced , the square of the side subtending the obtuse angle , is greater than the squares of the sides containing the obtuse angle , by twice the

**rectangle**contained by the side upon which , when produced ... Page 52

2 . the point D , the squares of CB , BD are equal * to twice the

2 . the point D , the squares of CB , BD are equal * to twice the

**rectangle**contained by CB , BD , and the square of DC : to each of these equals add the square of AD ; therefore the squares of CB , BD , DA , are equalt to twice the ...### 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