The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . XIX . A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . XX . Rectilineal ...
... semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . XIX . A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . XX . Rectilineal ...
Σελίδα 45
... semicircle bhf , and produce de to h , and join gh therefore because the straight line bf is divided into two equal parts in the point g , and into two unequal b مع g c But if they A a f at e , the rectangle be , ef , together with the ...
... semicircle bhf , and produce de to h , and join gh therefore because the straight line bf is divided into two equal parts in the point g , and into two unequal b مع g c But if they A a f at e , the rectangle be , ef , together with the ...
Σελίδα 59
... semicircle is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal angle . Q. E. D. COR . From this it is manifest , that the straight line which is drawn at right angles to the ...
... semicircle is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal angle . Q. E. D. COR . From this it is manifest , that the straight line which is drawn at right angles to the ...
Σελίδα 61
... semicircle , and join b f . fd : and because the angle bfd is at the centre , and the angle bad at the circumference , and that they have the same part of the circumference , viz . b c d for their base ; b therefore the angle bfd is ...
... semicircle , and join b f . fd : and because the angle bfd is at the centre , and the angle bad at the circumference , and that they have the same part of the circumference , viz . b c d for their base ; b therefore the angle bfd is ...
Σελίδα 62
... semicircle ; and the angles in it bac , bec are equal , by the first case for the same reason , because cbed is greater than a semicircle , the angles cad , ced , are equal therefore the whole angle bad is equal to the whole angle bed ...
... semicircle ; and the angles in it bac , bec are equal , by the first case for the same reason , because cbed is greater than a semicircle , the angles cad , ced , are equal therefore the whole angle bad is equal to the whole angle bed ...
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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