Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Edlemnts of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 86
... polygon , which is at once equilateral and equiangular , is called a regular polygon . Regular polygons may have any number of sides ; the equilateral tri- angle is one of three sides ; and the square is one of four sides . LEMMA . Any ...
... polygon , which is at once equilateral and equiangular , is called a regular polygon . Regular polygons may have any number of sides ; the equilateral tri- angle is one of three sides ; and the square is one of four sides . LEMMA . Any ...
Página 161
... polygon . Therefore , KL is the side of an equilateral polygon , described about the circle , of the same number of sides with the inscribed polygon ABCDEF . COR . 1. Because GL , GK , GN , and the other straight lines drawn . from the ...
... polygon . Therefore , KL is the side of an equilateral polygon , described about the circle , of the same number of sides with the inscribed polygon ABCDEF . COR . 1. Because GL , GK , GN , and the other straight lines drawn . from the ...
Página 162
... polygon M to the polygon N ; and , by conversion , he square of AC is to its excess above the squares of CF , that is , to the square of AF ( 37. 1. ) , as the polygon M to its excess above the polygon N. But the square of AC , that is ...
... polygon M to the polygon N ; and , by conversion , he square of AC is to its excess above the squares of CF , that is , to the square of AF ( 37. 1. ) , as the polygon M to its excess above the polygon N. But the square of AC , that is ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal arc AC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC wherefore