The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 32
... half of the parallelogram EBCA , because the dia- meter AB bisects * it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are * equal ; therefore the ...
... half of the parallelogram EBCA , because the dia- meter AB bisects * it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are * equal ; therefore the ...
Page 43
... half the line . Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D : the rectangle AD , DB , together with the square of CD , shall be equal to the square of CB . * Upon ...
... half the line . Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D : the rectangle AD , DB , together with the square of CD , shall be equal to the square of CB . * Upon ...
Page 44
... half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced . Let the straight line AB be bisected in C , and pro- duced to the point D : the rectangle AD , DB , together with ...
... half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced . Let the straight line AB be bisected in C , and pro- duced to the point D : the rectangle AD , DB , together with ...
Page 47
... half of a right angle . For the same reason each of the angles ČEB , EBC is half a right angle ; and therefore the whole AEB is a right angle . And because the angle GEF is half a right angle , and EGF a right angle , for it is equal to ...
... half of a right angle . For the same reason each of the angles ČEB , EBC is half a right angle ; and therefore the whole AEB is a right angle . And because the angle GEF is half a right angle , and EGF a right angle , for it is equal to ...
Page 48
... half the line bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in C , and pro- duced to the point D : the squares of AD , DB shall be double of the squares of AC ...
... half the line bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in C , and pro- duced to the point D : the squares of AD , DB shall be double of the squares of AC ...
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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