The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 29
... remaining complement bk is equal to the remaining complement k d Wherefore the complements , & c . Q. E. D. ... angle . LET ab be the given straight line , and c the given triangle , and d the given rectilineal angle . It is required to ...
... remaining complement bk is equal to the remaining complement k d Wherefore the complements , & c . Q. E. D. ... angle . LET ab be the given straight line , and c the given triangle , and d the given rectilineal angle . It is required to ...
Σελίδα 34
... angle and one of its opposite interior angles double of those in another triangle , its remaining opposite interior angle is also double of the corresponding angle in the other . 18. If two sides of a triangle be bisected , the straight ...
... angle and one of its opposite interior angles double of those in another triangle , its remaining opposite interior angle is also double of the corresponding angle in the other . 18. If two sides of a triangle be bisected , the straight ...
Σελίδα 41
... angle : and because the angle gef is half a right angle , and eg fa right angle , for it is equal ( i . 29 ) to the interior and opposite angle e cb , the remaining angle efg is half a right angle ; therefore the angle gef is equal to ...
... angle : and because the angle gef is half a right angle , and eg fa right angle , for it is equal ( i . 29 ) to the interior and opposite angle e cb , the remaining angle efg is half a right angle ; therefore the angle gef is equal to ...
Σελίδα 42
... angle eac ; and the angle ace is a right angle ; therefore each of the angles cea , eac is half a right angle ( i ... remaining angle dgb is half a right angle , and is therefore equal to the angle dbg ; wherefore also the side bd is ...
... angle eac ; and the angle ace is a right angle ; therefore each of the angles cea , eac is half a right angle ( i ... remaining angle dgb is half a right angle , and is therefore equal to the angle dbg ; wherefore also the side bd is ...
Σελίδα 43
Euclides. g h b of eb , because the angle eab is a right angle ; therefore ... remain- ing rectangle cf , fa , is equal to the square of ab ; and the ... angled triangles , if a perpendicular be drawn from any of the acute angles to the ...
Euclides. g h b of eb , because the angle eab is a right angle ; therefore ... remain- ing rectangle cf , fa , is equal to the square of ab ; and the ... angled triangles , if a perpendicular be drawn from any of the acute angles to the ...
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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