Elements of Geometry |
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Page v
... give to it all the exact- ness and precision of which it is susceptible . Perhaps I might have attained this object by calling a straight line that which can have only one position between two given points . For , from this essential ...
... give to it all the exact- ness and precision of which it is susceptible . Perhaps I might have attained this object by calling a straight line that which can have only one position between two given points . For , from this essential ...
Page xii
... gives also A : B :: C : D A : C :: B : D , and , since the ratios A : C , B : D , are equal , we obtain B + A : D + C :: A : Cor : : B : D , B - A : D C : A Cor : : B : D , - a result which may be thus enunciated . In any proportion ...
... gives also A : B :: C : D A : C :: B : D , and , since the ratios A : C , B : D , are equal , we obtain B + A : D + C :: A : Cor : : B : D , B - A : D C : A Cor : : B : D , - a result which may be thus enunciated . In any proportion ...
Page 47
... gives a quadruple square ( fig . 103 ) , a triple Fig . 103 . line a square nine times as great , and so on . THEOREM . 174. The area of any parallelogram is equal to the product of its base by its altitude . Demonstration . The ...
... gives a quadruple square ( fig . 103 ) , a triple Fig . 103 . line a square nine times as great , and so on . THEOREM . 174. The area of any parallelogram is equal to the product of its base by its altitude . Demonstration . The ...
Page 49
... gives BC = EF ; but , on account of the parallels , IG = BC , and DG EF , therefore HIGD is equal to the square described upon BC . These two parts being taken from the whole square , there remain the two rectangles BCGI , EFIH , which ...
... gives BC = EF ; but , on account of the parallels , IG = BC , and DG EF , therefore HIGD is equal to the square described upon BC . These two parts being taken from the whole square , there remain the two rectangles BCGI , EFIH , which ...
Page 51
... give the name of segment to that part of the hypothe- nuse cut off by the perpendicular let fall from the right angle ; thus BD is the segment adjacent to the side AB , and DC the segment adjacent to the side AC . We have likewise Fig ...
... give the name of segment to that part of the hypothe- nuse cut off by the perpendicular let fall from the right angle ; thus BD is the segment adjacent to the side AB , and DC the segment adjacent to the side AC . We have likewise Fig ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence