The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 11-15 of 73
Page 52
... rectangle CB , BD ; that is , the square of AC alone is less than the squares of CB , BA , by twice the rectangle CB , BD . Secondly , let AD fall without the triangle ABC : then , because the angle at D is a right angle , the angle ACB ...
... rectangle CB , BD ; that is , the square of AC alone is less than the squares of CB , BA , by twice the rectangle CB , BD . Secondly , let AD fall without the triangle ABC : then , because the angle at D is a right angle , the angle ACB ...
Page 53
... rectangle BE , EF , toge- ther with the square of EG , is equal to the squares of † 1 Ax . HE , EG : take away the square of EG , which is com- mon to both ; and the remaining rectangle BE , EF is equal to the square of EH : but the ...
... rectangle BE , EF , toge- ther with the square of EG , is equal to the squares of † 1 Ax . HE , EG : take away the square of EG , which is com- mon to both ; and the remaining rectangle BE , EF is equal to the square of EH : but the ...
Page 81
... rectangle contained by the segments of one of them , is equal to the rectangle contained by the segments of the other . Let the two straight lines AC , BD , cut one another in the point E within the circle ABCD : the rectangle contained ...
... rectangle contained by the segments of one of them , is equal to the rectangle contained by the segments of the other . Let the two straight lines AC , BD , cut one another in the point E within the circle ABCD : the rectangle contained ...
Page 82
... rectangle AE , EC , together with the square of EF , is equal to the square of AF ; that is , to the square of FB : but the square of FB is equal * to the rectangle BE , ED , together with the square of EF ; therefore the rectangle AE ...
... rectangle AE , EC , together with the square of EF , is equal to the square of AF ; that is , to the square of FB : but the square of FB is equal * to the rectangle BE , ED , together with the square of EF ; therefore the rectangle AE ...
Page 83
... rectangle AD , DC , to- gether with the square of EC , is equal to the square of ED : but CE is equal to EB ; therefore the rectangle AD , DC , to- gether with the square of EB , is equal to the square of ED : but the square of ED is ...
... rectangle AD , DC , to- gether with the square of EC , is equal to the square of ED : but CE is equal to EB ; therefore the rectangle AD , DC , to- gether with the square of EB , is equal to the square of ED : but the square of ED is ...
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