The Elements of Euclid |
From inside the book
Results 1-5 of 78
Page vi
... in the demonstration of the 26th prop . of the 11th book , it is taken for granted , that those solid angles are equal to one another which are contained by plane angles of the same number and magnitude , placed vi PREFACE .
... in the demonstration of the 26th prop . of the 11th book , it is taken for granted , that those solid angles are equal to one another which are contained by plane angles of the same number and magnitude , placed vi PREFACE .
Page 9
... taken , See N. the straight line between them lies wholly in that superficies . VIII . " A plane angle is the inclination of two lines to one another See N. " in a plane , which meet together , but are not in the same " direction . IX ...
... taken , See N. the straight line between them lies wholly in that superficies . VIII . " A plane angle is the inclination of two lines to one another See N. " in a plane , which meet together , but are not in the same " direction . IX ...
Page 13
... taken from equals , the remainders are equal . 1 If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , are equal to one ...
... taken from equals , the remainders are equal . 1 If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , are equal to one ...
Page 14
... taken together less " than two right angles , these straight lines being continually 66 produced , shall 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 ...
... taken together less " than two right angles , these straight lines being continually 66 produced , shall 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 ...
Page 69
... taken in the 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 circum- ference ; the straight line drawn from A to B shall fall within the ...
... taken in the 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 circum- ference ; the straight line drawn from A to B shall fall within the ...
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