The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 6
... angles shall be equal , each to each , viz . those to which the equal sides are opposite . b a ce d f def , and the angle acb to dfe . LET abc , def be two triangles , which have the two sides ab , ac equal to the two sides de , df ...
... angles shall be equal , each to each , viz . those to which the equal sides are opposite . b a ce d f def , and the angle acb to dfe . LET abc , def be two triangles , which have the two sides ab , ac equal to the two sides de , df ...
Σελίδα 7
... angle fag common to the two triangles afc , agb ; there- f d a b C g e fore the base fc is equal ( i . 4 ) to the ... acb , which are the angles at the base of the triangle abc : and it has also been proved that the angle fbc is ...
... angle fag common to the two triangles afc , agb ; there- f d a b C g e fore the base fc is equal ( i . 4 ) to the ... acb , which are the angles at the base of the triangle abc : and it has also been proved that the angle fbc is ...
Σελίδα 8
... acb , ad b , upon the same base a b , and upon the same side of it , which have their sides ca , da terminated in ... angle acd is equal ( i . 5 ) to the angle adc : but b the angle acd is greater than the angle bcd ; therefore the ...
... acb , ad b , upon the same base a b , and upon the same side of it , which have their sides ca , da terminated in ... angle acd is equal ( i . 5 ) to the angle adc : but b the angle acd is greater than the angle bcd ; therefore the ...
Σελίδα 13
Euclides. are equal to the angles aed , deb . Take away the common angle aed , and the remaining angle cea is equal ... acb ; therefore the angles acd , acb are greater than the angles abc , acb ; butacd , acb are together equal ( i ...
Euclides. are equal to the angles aed , deb . Take away the common angle aed , and the remaining angle cea is equal ... acb ; therefore the angles acd , acb are greater than the angles abc , acb ; butacd , acb are together equal ( i ...
Σελίδα 14
... 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 side of every triangle is opposite to the greater angle . a LET abc be a triangle , of ...
... 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 side of every triangle is opposite to the greater angle . a LET abc be a triangle , of ...
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ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle