The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 45
... , viz . by applying ( 44. 1. ) to the given straight line a parallelogram equal to the first triangle ABD , and having an angle equal to the given angle . PROP . XLVI . PROB . To describe a square BOOK I. 45 THE ELEMENTS OF EUCLID .
... , viz . by applying ( 44. 1. ) to the given straight line a parallelogram equal to the first triangle ABD , and having an angle equal to the given angle . PROP . XLVI . PROB . To describe a square BOOK I. 45 THE ELEMENTS OF EUCLID .
Side 46
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( 11. 1. ) AC at right angles to AB ; and make ( 3. 1. ) AD equal to ÁB , and through the point ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( 11. 1. ) AC at right angles to AB ; and make ( 3. 1. ) AD equal to ÁB , and through the point ...
Side 47
... square GB and in the same manner , by joining AE , BK , it is demonstrated that the paralle- logram CL is equal to the square HC : therefore the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is described ...
... square GB and in the same manner , by joining AE , BK , it is demonstrated that the paralle- logram CL is equal to the square HC : therefore the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is described ...
Side 48
... square described upon BC , one of the sides of the tri- angle ABC , be equal to the squares upon the other sides BA ... square of DA is equal to the square of AB : to each of these add the square of AC : therefore the squares of DA , AC ...
... square described upon BC , one of the sides of the tri- angle ABC , be equal to the squares upon the other sides BA ... square of DA is equal to the square of AB : to each of these add the square of AC : therefore the squares of DA , AC ...
Side 50
... square ADEB , and through C draw ( 31. 1. ) CF , parallel to AD or BE ; then AE is equal to the rectangles AF , CE : and AE is the square of AB : and AF is the rectangle contained by с в F ⚫N . B. To avoid repeating the word contained ...
... square ADEB , and through C draw ( 31. 1. ) CF , parallel to AD or BE ; then AE is equal to the rectangles AF , CE : and AE is the square of AB : and AF is the rectangle contained by с в F ⚫N . B. To avoid repeating the word contained ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone 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 meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment 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