The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 17
... less to the greater ; which is impossible : therefore two straight lines cannot have a common segment . PROP . XII . PROB . To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point ...
... less to the greater ; which is impossible : therefore two straight lines cannot have a common segment . PROP . XII . PROB . To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point ...
Page 21
... less than two right angles . Let ABC be any triangle ; any two of its angles together shall be less than two right angles . B Produce BC to D ; and be- cause ACD 294989.
... less than two right angles . Let ABC be any triangle ; any two of its angles together shall be less than two right angles . B Produce BC to D ; and be- cause ACD 294989.
Page 22
... less than two right angles . In like manner , it may be demonstrated , that BAC , ACB , as also CÁB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. * 3 . 1 . 5. 1 . PROP . XVIII . THEOR . * The greater ...
... less than two right angles . In like manner , it may be demonstrated , that BAC , ACB , as also CÁB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. * 3 . 1 . 5. 1 . PROP . XVIII . THEOR . * The greater ...
Page 23
... less than it it is not equal , because then the angle ABC would be equal * * 5.1 to the angle CAB ; but it is † not ; therefore † Hyp AC is not equal to AB : nei- ther is it less ; because then the angle ABC would be less * than the ...
... less than it it is not equal , because then the angle ABC would be equal * * 5.1 to the angle CAB ; but it is † not ; therefore † Hyp AC is not equal to AB : nei- ther is it less ; because then the angle ABC would be less * than the ...
Page 24
... less than the other two sides of the triangle , but shall contain a greater angle . Let ABC be a triangle , and from the points B , C , the ends of the side BC , let the two straight lines BD , CD be drawn to the point D within the ...
... less than the other two sides of the triangle , but shall contain a greater angle . Let ABC be a triangle , and from the points B , C , the ends of the side BC , let the two straight lines BD , CD be drawn to the point D within the ...
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