The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 2
... angle at a point , it may be expressed by a letter placed at that point ; as the angle at e . X. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right ...
... angle at a point , it may be expressed by a letter placed at that point ; as the angle at e . X. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right ...
Página 3
... equal sides . XXV . An isosceles triangle is that which has only two sides equal . Δ Δ Δ Equilateral . Isosceles ... angle . XXVIII . An obtuse - angled triangle is that which has an obtuse angle . Right - angled .. Obtuse - angled ...
... equal sides . XXV . An isosceles triangle is that which has only two sides equal . Δ Δ Δ Equilateral . Isosceles ... angle . XXVIII . An obtuse - angled triangle is that which has an obtuse angle . Right - angled .. Obtuse - angled ...
Página 5
... angle abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the ...
... angle abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the ...
Página 6
... equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . b a се d f def , and the angle a cb to dfe . LET abc , def be two triangles ...
... equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . b a се d f def , and the angle a cb to dfe . LET abc , def be two triangles ...
Página 7
... equal ( i . 3 ) to a f , the less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the two sides fa , a c are equal to the two ga , ab , each to each ; and they contain the angle ... equal ( i . 4 ) to the ...
... equal ( i . 3 ) to a f , the less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the two sides fa , a c are equal to the two ga , ab , each to each ; and they contain the angle ... equal ( i . 4 ) 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