The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 1-5 of 91
Page 5
... called Trapeziums . XXXV . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted , that a B 3 BOOK I. - DEFINITIONS . 5 XXX. ...
... called Trapeziums . XXXV . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted , that a B 3 BOOK I. - DEFINITIONS . 5 XXX. ...
Page 30
... parallel * to one another : therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXVIII . THEOR . If a straight line falling upon two other straight lines makes the exterior angle equal to the in ...
... parallel * to one another : therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXVIII . THEOR . If a straight line falling upon two other straight lines makes the exterior angle equal to the in ...
Page 31
... parallel to CD . Because the angle EGB is equal to the angle GHD , A- -B -D + Hyp and the angle EGB equal * , to the angle AGH , * 15 . 1 . therefore the angle AGH is equal † to the angle +1 Ax . GHD : and they are the alternate angles ...
... parallel to CD . Because the angle EGB is equal to the angle GHD , A- -B -D + Hyp and the angle EGB equal * , to the angle AGH , * 15 . 1 . therefore the angle AGH is equal † to the angle +1 Ax . GHD : and they are the alternate angles ...
Page 32
... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . 4 Let the straight line GHK eut AB , EF , CD : and because GHK cuts the parallel straight lines AB ...
... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . 4 Let the straight line GHK eut AB , EF , CD : and because GHK cuts the parallel straight lines AB ...
Page 33
... parallel to CD . * 27 . 1 . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB . * To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given straight line ...
... parallel to CD . * 27 . 1 . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB . * To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given straight line ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole