The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 33
... inscribe a square in a parallelogram .. 12. Given a right - angled isosceles triangle to inscribe in it a square . 13. Given a finite straight line to describe a square of which that line Ishall be the diameter . 14. To construct a ...
... inscribe a square in a parallelogram .. 12. Given a right - angled isosceles triangle to inscribe in it a square . 13. Given a finite straight line to describe a square of which that line Ishall be the diameter . 14. To construct a ...
Página 76
... inscribe a triangle 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 ) ...
... inscribe a triangle 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 ) ...
Página 77
... : wherefore the triangle 1mn is equiangular to the triangle def : and it is described about the circle a b c Which was to be done . m b e 1 g f h PROPOSITION IV . - PROBLEM . To inscribe a circle BOOK IV . PROP . III . 77.
... : wherefore the triangle 1mn is equiangular to the triangle def : and it is described about the circle a b c Which was to be done . m b e 1 g f h PROPOSITION IV . - PROBLEM . To inscribe a circle BOOK IV . PROP . III . 77.
Página 78
Euclides. PROPOSITION IV . - PROBLEM . To inscribe a circle in a given triangle . LET the given triangle be a bc ; it is required to inscribe a circle in abc . Bisect ( i . 9 ) the angles abc , bca by the straight lines b d , cd meet ...
Euclides. PROPOSITION IV . - PROBLEM . To inscribe a circle in a given triangle . LET the given triangle be a bc ; it is required to inscribe a circle in abc . Bisect ( i . 9 ) the angles abc , bca by the straight lines b d , cd meet ...
Página 79
... inscribe a square in a given circle . LET abcd be the given circle ; it is required to inscribe a square in abcd . Draw the diameters a c , bd , at right angles to one another , and join ab , bc , cd , da ; because be is equal to ed ...
... inscribe a square in a given circle . LET abcd be the given circle ; it is required to inscribe a square in abcd . Draw the diameters a c , bd , at right angles to one another , and join ab , bc , cd , da ; because be is equal to ed ...
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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