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, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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... passing through the hands of the ancient editors during the decline of science , had suffered some diminution of their excellence , and much skill and learning have been employed by the modern mathemati- cians to deliver them from ...
... passing through the hands of the ancient editors during the decline of science , had suffered some diminution of their excellence , and much skill and learning have been employed by the modern mathemati- cians to deliver them from ...
Página 30
... passes , and let BK , KD be the other parallelo- grams , which make up the whole figure ABCD , and are therefore called the com- plements ; The complement BK is equal to the complement KD . H D E / K F B G Because ABCD is a ...
... passes , and let BK , KD be the other parallelo- grams , which make up the whole figure ABCD , and are therefore called the com- plements ; The complement BK is equal to the complement KD . H D E / K F B G Because ABCD is a ...
Página 57
... pass through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . Let ABC be a circle , and let CD , a straight line drawn through the cen- tre , bisect any straight line AB , which ...
... pass through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . Let ABC be a circle , and let CD , a straight line drawn through the cen- tre , bisect any straight line AB , which ...
Página 58
... pass through the centre : AC , BD do not bisect one another . A D For if it is possible , let AE be equal to EC , and BE to ED ; If one of the lines pass through the centre , it is plain that it cannot be bisected by the other , which ...
... pass through the centre : AC , BD do not bisect one another . A D For if it is possible , let AE be equal to EC , and BE to ED ; If one of the lines pass through the centre , it is plain that it cannot be bisected by the other , which ...
Página 59
... passing through the centre is always greater than one more remote from it ; And from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a ...
... passing through the centre is always greater than one more remote from it ; And from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided 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 triangle DEF wherefore