The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 37
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . * * C * 44. 1 . * 11. 1 . * 3. 1 . * 31. 1 . 1 . * 34.1 . † Constr . From the point A draw * AC at right angles to AB ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . * * C * 44. 1 . * 11. 1 . * 3. 1 . * 31. 1 . 1 . * 34.1 . † Constr . From the point A draw * AC at right angles to AB ...
Page 38
... square , and it is described upon the given straight line AB . Which was to be done . 46. 1 . * 31. 1 . † Hyp . * 30 ... AC . On BC describe the square_BDEC , and on BA , AC the squares GB , HC ; and through A draw * AL parallel to BD ...
... square , and it is described upon the given straight line AB . Which was to be done . 46. 1 . * 31. 1 . † Hyp . * 30 ... AC . On BC describe the square_BDEC , and on BA , AC the squares GB , HC ; and through A draw * AL parallel to BD ...
Page 39
... squares GB , HC upon BA , AC ; therefore the square upon the side BC is equal to the squares upon the sides BA , AC . Therefore , in any right - angled triangle , & c . Q. E. D. PROP . XLVIII . THEOR . If the square described upon one ...
... squares GB , HC upon BA , AC ; therefore the square upon the side BC is equal to the squares upon the sides BA , AC . Therefore , in any right - angled triangle , & c . Q. E. D. PROP . XLVIII . THEOR . If the square described upon one ...
Page 41
... AC shall be equal to the square of AB . C B * 46.1 . * 31 . 1 . Upon AB describe the square ADEB , and through C draw * CF , parallel to AD or BE . Then AE is equal to the rectan- gles AF , CE : but AE is the square of AB ; and AF is ...
... AC shall be equal to the square of AB . C B * 46.1 . * 31 . 1 . Upon AB describe the square ADEB , and through C draw * CF , parallel to AD or BE . Then AE is equal to the rectan- gles AF , CE : but AE is the square of AB ; and AF is ...
Page 42
... square of the aforesaid part . Let the straight line AB be divided into any two parts in the point C : the rectangle AB , BC shall be equal to the rectangle AC , CB , together with the square of BC . * B E Upon BC describe the square ...
... square of the aforesaid part . Let the straight line AB be divided into any two parts in the point C : the rectangle AB , BC shall be equal to the rectangle AC , CB , together with the square of BC . * B E Upon BC describe the square ...
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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