The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 1-5 of 74
Page 3
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference , are equal to one another . Д XVI . And this point is called the centre of the circle . XVII . A diameter of a circle ...
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference , are equal to one another . Д XVI . And this point is called the centre of the circle . XVII . A diameter of a circle ...
Page 54
... circumferences are equal . " This is not a definition , but a theorem , the truth of which is evident ; for , if the circles be applied to one another , so that their centres coincide , the circles must likewise coincide , since the ...
... circumferences are equal . " This is not a definition , but a theorem , the truth of which is evident ; for , if the circles be applied to one another , so that their centres coincide , the circles must likewise coincide , since the ...
Page 55
... circumference it cuts off . VII . " The angle of a segment is that which is contained by the straight line and the circumference . " VIII . An angle in a segment is the angle con- tained by two straight lines drawn from any point in the ...
... circumference it cuts off . VII . " The angle of a segment is that which is contained by the straight line and the circumference . " VIII . An angle in a segment is the angle con- tained by two straight lines drawn from any point in the ...
Page 56
... circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle . N. B. ...
... circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle . N. B. ...
Page 57
... circumference AB take any point F , join DF , and produce it to E : then because DA is equal + to DB , the angle DAB is equal * D 1. 3 . † 15 Def . 1 . 5. 1 . to the angle DBA : and because AE , a side of the tri- angle DAE , is ...
... circumference AB take any point F , join DF , and produce it to E : then because DA is equal + to DB , the angle DAB is equal * D 1. 3 . † 15 Def . 1 . 5. 1 . to the angle DBA : and because AE , a side of the tri- angle DAE , 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