The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 1
... meet together , but are not in the same direction . IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . d b e N.B. When several angles ...
... meet together , but are not in the same direction . IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . d b e N.B. When several angles ...
Σελίδα 3
... besides these are called trape- ziums . 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 straight DEFINITIONS . 3.
... besides these are called trape- ziums . 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 straight DEFINITIONS . 3.
Σελίδα 4
... meets two straight lines , so as to make the two interior angles on the same side of it taken together less than two right angles , these straight lines being continually produced , shall at length meet upon that side on which are the ...
... meets two straight lines , so as to make the two interior angles on the same side of it taken together less than two right angles , these straight lines being continually produced , shall at length meet upon that side on which are the ...
Σελίδα 11
... meet- ing a bin f , g ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch , drawn from the given point c , is perpendicular to the given straight line a b a h f d g b Because fh is equal to hg , and he common ...
... meet- ing a bin f , g ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch , drawn from the given point c , is perpendicular to the given straight line a b a h f d g b Because fh is equal to hg , and he common ...
Σελίδα 20
... meet towards b , d . In like manner it may be 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 ...
... meet towards b , d . In like manner it may be 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 ...
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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