The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 6-10 of 28
Page 342
... difference AC of two magnitudes AB , BC , which have a given ratio be given ; each of the magni- tudes AB , BC , is given . PROP . IX . Magnitudes which have given ratios to the same magni- tude , have also a given ratio to one another ...
... difference AC of two magnitudes AB , BC , which have a given ratio be given ; each of the magni- tudes AB , BC , is given . PROP . IX . Magnitudes which have given ratios to the same magni- tude , have also a given ratio to one another ...
Page 401
... difference of the sides which contain the given angle , is less than the square of the third side , shall have a given ratio to the triangle . This is demonstrated the same way as in the preceding proposition , by help of the second ...
... difference of the sides which contain the given angle , is less than the square of the third side , shall have a given ratio to the triangle . This is demonstrated the same way as in the preceding proposition , by help of the second ...
Page 416
... difference of the straight lines be given , they shall each of them be given . Let AB , BC , contain the parallelogram AC given in magnitude , in the given angle ABC , and let the excess of BC above AB be given ; each of the straight ...
... difference of the straight lines be given , they shall each of them be given . Let AB , BC , contain the parallelogram AC given in magnitude , in the given angle ABC , and let the excess of BC above AB be given ; each of the straight ...
Page 434
... difference of a right angle , and the angle contained by the straight line given in posi- tion , and the straight line which joins the given point and the centre of the circle ; and from the point in which the second line meets the ...
... difference of a right angle , and the angle contained by the straight line given in posi- tion , and the straight line which joins the given point and the centre of the circle ; and from the point in which the second line meets the ...
Page 457
... and secant , may be found . VIII . The difference of an angle from a right angle , is called Fig . 3 . the complement of that angle . Thus , if BH be drawn perpendicular to AB , the angle CBH will be the PLANE TRIGONOMETRY . 457.
... and secant , may be found . VIII . The difference of an angle from a right angle , is called Fig . 3 . the complement of that angle . Thus , if BH be drawn perpendicular to AB , the angle CBH will be the PLANE TRIGONOMETRY . 457.
Other editions - View all
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