Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 sider |
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Side 183
... 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 an isosceles triangle FGH , having each of the angles at G , H double of the ...
... 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 an isosceles triangle FGH , having each of the angles at G , H double of the ...
Side 184
... pentagon required . Because each of the angles ACD , CDA is double of CAD , and that they are bisected by the straight lines CE , DB ; therefore the five angles DAC , ACE , ECD , CDB , BDA are equal to one another : but equal angles ...
... pentagon required . Because each of the angles ACD , CDA is double of CAD , and that they are bisected by the straight lines CE , DB ; therefore the five angles DAC , ACE , ECD , CDB , BDA are equal to one another : but equal angles ...
Side 185
... HK double of BK , therefore HK is equal to KL : ( ax . 6. ) in like manner it may be shewn that GH , GM , ML are each of them equal to HK , or KL : therefore the pentagon GHKLM is equilateral . It is also BOOK IV . PROP . XII . 185.
... HK double of BK , therefore HK is equal to KL : ( ax . 6. ) in like manner it may be shewn that GH , GM , ML are each of them equal to HK , or KL : therefore the pentagon GHKLM is equilateral . It is also BOOK IV . PROP . XII . 185.
Side 186
... pentagon GHKLM is equiangular : and it is equilateral , as was demonstrated ; and it is described about the circle ABCDE . PROPOSITION XIII . PROBLEM . Q.E.F. To inscribe a circle in a given equilateral and equiangular pentagon . Let ...
... pentagon GHKLM is equiangular : and it is equilateral , as was demonstrated ; and it is described about the circle ABCDE . PROPOSITION XIII . PROBLEM . Q.E.F. To inscribe a circle in a given equilateral and equiangular pentagon . Let ...
Side 187
... pentagon . Let ABCDE be the given equilateral and equiangular pentagon . It is required to describe a circle about ABCDE . B A E Bisect the angles BCD , CDE by the straight lines CF , FD , ( 1. 9. ) and from the point F , in which they ...
... pentagon . Let ABCDE be the given equilateral and equiangular pentagon . It is required to describe a circle about ABCDE . B A E Bisect the angles BCD , CDE by the straight lines CF , FD , ( 1. 9. ) and from the point F , in which they ...
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A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
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