The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 6
... angle bac equal to the angle edf , the base bc shall be equal to the base ef ; and the triangle abc to the triangle def ; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle abc ...
... angle bac equal to the angle edf , the base bc shall be equal to the base ef ; and the triangle abc to the triangle def ; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle abc ...
Seite 9
... angle bac coincides with the angle e df , and is equal ( Sax . ) to it . Therefore if two triangles , & c . Q.E.D. PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac ...
... angle bac coincides with the angle e df , and is equal ( Sax . ) to it . Therefore if two triangles , & c . Q.E.D. PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac ...
Seite 13
Euclides. are equal to the angles aed , deb . Take away the common angle a ed , and the remaining angle cea is equal ... bac . Bisect ( i . 10 ) ac in e , join be and produce it to f , and make e f equal to be ; join also fc , and produce ac ...
Euclides. are equal to the angles aed , deb . Take away the common angle a ed , and the remaining angle cea is equal ... bac . Bisect ( i . 10 ) ac in e , join be and produce it to f , and make e f equal to be ; join also fc , and produce ac ...
Seite 14
... 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 side of every triangle is opposite to the greater angle . d LET abc be a triangle ...
... 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 side of every triangle is opposite to the greater angle . d LET abc be a triangle ...
Seite 15
... angle bed of the triangle dcb is greater than its angle bdc , and that the ... bac . a e Produce bd to e ; and because two sides of a triangle are greater ... angle of a triangle is greater than the interior and opposite angle , the ...
... angle bed of the triangle dcb is greater than its angle bdc , and that the ... bac . a e Produce bd to e ; and because two sides of a triangle are greater ... angle of a triangle is greater than the interior and opposite angle , 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