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 sider |
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Resultat 6-10 av 62
Side 38
... describe a parallelogram that shall be equal to the given trian- gle ABC , and have one of its angles equal to D. Bisect ( Prob . 5. ) BC in E , join AE , and at the point E in the straight A F G line EC make ( Prob . 9. 38 ELEMENTS.
... describe a parallelogram that shall be equal to the given trian- gle ABC , and have one of its angles equal to D. Bisect ( Prob . 5. ) BC in E , join AE , and at the point E in the straight A F G line EC make ( Prob . 9. 38 ELEMENTS.
Side 48
... bisected , and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of half the line bisected , is equal to the square of the straight line which is ...
... bisected , and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of half the line bisected , is equal to the square of the straight line which is ...
Side 51
... bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC , CD . From the point ...
... bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC , CD . From the point ...
Side 53
... bisected , the sum of the squares of the other two sides is double of the square of half the side bisected , and of the square of the line drawn from the point of bisection to the opposite angle of the triangle . Let ABC be a triangle ...
... bisected , the sum of the squares of the other two sides is double of the square of half the side bisected , and of the square of the line drawn from the point of bisection to the opposite angle of the triangle . Let ABC be a triangle ...
Side 54
... bisected in E , AB2 + AD2 = ( A . 2. ) 2BE2 + 2AE2 ; and for the same reason , CD2 + BC2 = 2BE2 + 2EC2 = 2BE2 + 2AE2 , because ECAE . Therefore AB2 + AD2 + DC2 + BC2 = 4BE2 + 4AE2 . But 4BE2 = BD2 , and 4AE2 - AC2 ( 2 Cor . 8. 2 ...
... bisected in E , AB2 + AD2 = ( A . 2. ) 2BE2 + 2AE2 ; and for the same reason , CD2 + BC2 = 2BE2 + 2EC2 = 2BE2 + 2AE2 , because ECAE . Therefore AB2 + AD2 + DC2 + BC2 = 4BE2 + 4AE2 . But 4BE2 = BD2 , and 4AE2 - AC2 ( 2 Cor . 8. 2 ...
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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