The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 39
... described upon one of the sides of a triangle , be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . Let the square described upon BC , one of the sides of the ...
... described upon one of the sides of a triangle , be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . Let the square described upon BC , one of the sides of the ...
Page 53
... described upon EH shall be equal to the given rectilineal figure A. * * 47.1 . Join GH : and because the straight line BF is di- vided into two equal parts in the point G , and into two unequal at E , the rectangle BE , EF , together ...
... described upon EH shall be equal to the given rectilineal figure A. * * 47.1 . Join GH : and because the straight line BF is di- vided into two equal parts in the point G , and into two unequal at E , the rectangle BE , EF , together ...
Page 73
... described : and because the centre D is in AC , the segment ABC , A4 A E 9.3 . is a semicircle . But if the angles ABD , BAD are not equal to one another , at the point A , in the straight + See Fig . 2. and 3 . * 23. 1 . line AB , make ...
... described : and because the centre D is in AC , the segment ABC , A4 A E 9.3 . is a semicircle . But if the angles ABD , BAD are not equal to one another , at the point A , in the straight + See Fig . 2. and 3 . * 23. 1 . line AB , make ...
Page 74
... described . And it is evident , that if the angle ABD be + SeeFig . 2. greater + than the angle BAD , the centre E falls with- * 9 . 3 . out the segment ABC , which therefore is less than a + See Fig.3 . semicircle : but if the angle ...
... described . And it is evident , that if the angle ABD be + SeeFig . 2. greater + than the angle BAD , the centre E falls with- * 9 . 3 . out the segment ABC , which therefore is less than a + See Fig.3 . semicircle : but if the angle ...
Page 80
... described from the centre G , at the dis- tance GA , shall pass through the point B : let this be the circle AHB . The segment AHB shall contain an angle equal to the given rectilineal angle C. H A B E D ' * Because from the point A ...
... described from the centre G , at the dis- tance GA , shall pass through the point B : let this be the circle AHB . The segment AHB shall contain an angle equal to the given rectilineal angle C. H A B E D ' * Because from the point A ...
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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