The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 45
... rectangle AD , DB : add to each of these LG , which is equal + to the square of CB ; therefore the rectangle AD , DB , to- gether with the square of CB , is equal + to the gnomon CMG , and the figure LG : but the gnomon CMG and LG make ...
... rectangle AD , DB : add to each of these LG , which is equal + to the square of CB ; therefore the rectangle AD , DB , to- gether with the square of CB , is equal + to the gnomon CMG , and the figure LG : but the gnomon CMG and LG make ...
Page 46
... 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 of the whole and that part . Let the straight line AB be divided ...
... 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 of the whole and that part . Let the straight line AB be divided ...
Page 47
... 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 , is equal ...
... 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 , is equal ...
Page 50
... rectangle contained by the whole , and one of the parts , shall be equal to the square of the other part . * Upon AB ... rectangle CF , FA together with the square of AE , is equal to the square of EF : but EF is equal to EB ; therefore ...
... rectangle contained by the whole , and one of the parts , shall be equal to the square of the other part . * Upon AB ... rectangle CF , FA together with the square of AE , is equal to the square of EF : but EF is equal to EB ; therefore ...
Page 51
... rectangle BC , CD . * B * 4.2 . † 2 Ax . Because the straight line BD is di- vided into two parts in the point C , the square of BD is equal to the squares of BC , CD , and twice the rectangle BC , CD : to each of these equals add the ...
... rectangle BC , CD . * B * 4.2 . † 2 Ax . Because the straight line BD is di- vided into two parts in the point C , the square of BD is equal to the squares of BC , CD , and twice the rectangle BC , CD : to each of these equals add the ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn 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