The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 1-5 of 100
Page vi
... demonstrated , and not assumed ; and therefore , though this were a true proposition , it ought to have been demonstrated . But indeed this Proposition , which makes the 10th de- finition of the 11th Book , is not true universally , ex ...
... demonstrated , and not assumed ; and therefore , though this were a true proposition , it ought to have been demonstrated . But indeed this Proposition , which makes the 10th de- finition of the 11th Book , is not true universally , ex ...
Page 9
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
Page 10
... demonstrated , that the whole an- gle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ABC is equal + to the remaining angle ACB , which are the angles at the base ...
... demonstrated , that the whole an- gle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ABC is equal + to the remaining angle ACB , which are the angles at the base ...
Page 11
... demonstrated to be greater than it , which is impossible . EF But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F : therefore , because AC is equal † to AD in the tri- angle ACD , the angles ...
... demonstrated to be greater than it , which is impossible . EF But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F : therefore , because AC is equal † to AD in the tri- angle ACD , the angles ...
Page 16
... demonstrated , that no other can be in the same straight line with it but BD , which , therefore , is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. * PROP . XV . THEOR . If two straight lines cut one ...
... demonstrated , that no other can be in the same straight line with it but BD , which , therefore , is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. * PROP . XV . THEOR . If two straight lines cut one ...
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