The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 10
... manner , because abd is a straight line , the angle dbe is equal to the angle eba ; wherefore the angle dbe is C equal to the angle cbe , the less to the greater , which is impossible ; therefore two straight lines cannot have a common ...
... manner , because abd is a straight line , the angle dbe is equal to the angle eba ; wherefore the angle dbe is C equal to the angle cbe , the less to the greater , which is impossible ; therefore two straight lines cannot have a common ...
Σελίδα 12
... manner it may be demonstrated , that no other can be in the same straight line with it but bd , which therefore is in the same straight line with c b . Wherefore , if at a point , & c . Q. E. D. PROPOSITION XV . THEOREM . If two ...
... manner it may be demonstrated , that no other can be in the same straight line with it but bd , which therefore is in the same straight line with c b . Wherefore , if at a point , & c . Q. E. D. PROPOSITION XV . THEOREM . If two ...
Σελίδα 13
... manner it can be demonstrated , that the angles ceb , aed are equal . Therefore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that , if two straight lines cut one another , the angles they make at the ...
... manner it can be demonstrated , that the angles ceb , aed are equal . Therefore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that , if two straight lines cut one another , the angles they make at the ...
Σελίδα 14
Euclides. less than two right angles . In like manner it may be demonstrated , that bac , acb , as also cab , abc , are less than two right angles . There- fore any two angles , & c . Q. E. D. PROPOSITION XVIII . — THEOREM . The greater ...
Euclides. less than two right angles . In like manner it may be demonstrated , that bac , acb , as also cab , abc , are less than two right angles . There- fore any two angles , & c . Q. E. D. PROPOSITION XVIII . — THEOREM . The greater ...
Σελίδα 15
... manner it may be demonstrated , that the sides b , bc , are greater bc , ca greater than a b . two sides , & c . Q. E. D. than ca , and b Therefore any ల PROPOSITION XXI . - THEOREM . If from the ends of the side of a triangle there be ...
... manner it may be demonstrated , that the sides b , bc , are greater bc , ca greater than a b . two sides , & c . Q. E. D. than ca , and b Therefore any ల PROPOSITION XXI . - THEOREM . If from the ends of the side of a triangle there be ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle