The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 13
... 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 point where they cut ...
... 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 point where they cut ...
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
... 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 drawn two ...
... 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 drawn two ...
Σελίδα 20
... demonstrated , that they do not meet towards a , c , but those straight lines which meet neither way , though produced ever so far , are parallel ( 35 def . ) to one another . ab there- fore is parallel to cd . Wherefore , if a straight ...
... demonstrated , that they do not meet towards a , c , but those straight lines which meet neither way , though produced ever so far , are parallel ( 35 def . ) to one another . ab there- fore is parallel to cd . Wherefore , if a straight ...
Σελίδα 27
... demonstrated , that no b d other line but ad is parallel to bc ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. PROPOSITION XL . — THEOREM . Equal triangles upon equal bases , in the same straight line and ...
... demonstrated , that no b d other line but ad is parallel to bc ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. PROPOSITION XL . — THEOREM . Equal triangles upon equal bases , in the same straight line and ...
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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