The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 7
... equiangular . PROPOSITION VI . — THEOREM . e If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall also be equal to one another . LET abc be a triangle having the ...
... equiangular . PROPOSITION VI . — THEOREM . e If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall also be equal to one another . LET abc be a triangle having the ...
Σελίδα 76
... equiangular to a given triangle . LET a b c be the given circle , and def the given triangle ; it is required to inscribe in the circle abc a tri- angle equiangular to the triangle g d SH f b h def Draw ( iii . 17 ) the straight line ...
... equiangular to a given triangle . LET a b c be the given circle , and def the given triangle ; it is required to inscribe in the circle abc a tri- angle equiangular to the triangle g d SH f b h def Draw ( iii . 17 ) the straight line ...
Σελίδα 77
... equiangular to the triangle def , and it is inscribed in the circle abc . Which was to be done . PROPOSITION III . — PROBLEM . About a given circle to describe a triangle equiangular to a given triangle . LET abc be the given circle ...
... equiangular to the triangle def , and it is inscribed in the circle abc . Which was to be done . PROPOSITION III . — PROBLEM . About a given circle to describe a triangle equiangular to a given triangle . LET abc be the given circle ...
Σελίδα 82
... equiangular pentagon in a given circle . LET abcde be the given circle ; it is required to inscribe an equilateral and equiangular pentagon in the circle abcde . Describe ( iv . 10 ) an isosceles triangle f g h , having each of the ...
... equiangular pentagon in a given circle . LET abcde be the given circle ; it is required to inscribe an equilateral and equiangular pentagon in the circle abcde . Describe ( iv . 10 ) an isosceles triangle f g h , having each of the ...
Σελίδα 83
... equiangular ; and it has been shewn that it is equilateral . Wherefore , in the given circle , an equilateral and equiangular pentagon has been inscribed . Which was to be done . PROPOSITION XII . - PROBLEM . To describe an equilateral ...
... equiangular ; and it has been shewn that it is equilateral . Wherefore , in the given circle , an equilateral and equiangular pentagon has been inscribed . Which was to be done . PROPOSITION XII . - PROBLEM . To describe an equilateral ...
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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