The Elements of Euclid |
From inside the book
Page v
... propositions , as well as their demonstrations , to Theon ; others think the propositions to be Euclid's , but that the demonstrations are Theon's ; and others maintain that all the propositions and their demonstrations are Euclid's own ...
... propositions , as well as their demonstrations , to Theon ; others think the propositions to be Euclid's , but that the demonstrations are Theon's ; and others maintain that all the propositions and their demonstrations are Euclid's own ...
Page vi
... proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and , there- fore , though this were a true proposition , it ought to have been demonstrated . But ...
... proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and , there- fore , though this were a true proposition , it ought to have been demonstrated . But ...
Page vii
... propositions of it ; and , upon the 25th and 26th depend other eight , viz . the 27th , 31st , 32d , 33d , 34th ... proposition 17 , and prop . 18th of the 12th book , depend upon the 9th defini- tion of the 11th book , which is not ...
... propositions of it ; and , upon the 25th and 26th depend other eight , viz . the 27th , 31st , 32d , 33d , 34th ... proposition 17 , and prop . 18th of the 12th book , depend upon the 9th defini- tion of the 11th book , which is not ...
Page viii
... proposition concerning a proper- ty of quadrilateral figures in a circle is added at the end of the sixth book . Also the note on the 29th prop . book 1st , is altered , and made more explicit , and a more general demon- stration is ...
... proposition concerning a proper- ty of quadrilateral figures in a circle is added at the end of the sixth book . Also the note on the 29th prop . book 1st , is altered , and made more explicit , and a more general demon- stration is ...
Page 14
... at length meet upon that side on which are " the angles which are less than two right angles . See the " notes on prop . 29. of Book I. " PROPOSITION I. PROBLEM . TO describe an equilateral triangle upon 14 THE ELEMENTS.
... at length meet upon that side on which are " the angles which are less than two right angles . See the " notes on prop . 29. of Book I. " PROPOSITION I. PROBLEM . TO describe an equilateral triangle upon 14 THE ELEMENTS.
Other editions - View all
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore