Elements of Geometry and Trigonometry |
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Page 75
... parallelogram ADKL , and is measured by EFX AL . But we have AL - DK ; and since the triangles IBL and KCI are equal , the side BL = CK : hence , AB + CD = AL + DK = 2AL ; hence AL is the half sum of the bases AB , CD ; hence the area ...
... parallelogram ADKL , and is measured by EFX AL . But we have AL - DK ; and since the triangles IBL and KCI are equal , the side BL = CK : hence , AB + CD = AL + DK = 2AL ; hence AL is the half sum of the bases AB , CD ; hence the area ...
Page 81
... parallelogram the squares of the sides are together equivalent to the squares of the diagonals . For the diagonals AC , BD , bisect each B other ( Book I. Prop . XXXI . ) ; consequently the triangle ABC gives AB2 + BC - 2AE2 + 2BE2 ...
... parallelogram the squares of the sides are together equivalent to the squares of the diagonals . For the diagonals AC , BD , bisect each B other ( Book I. Prop . XXXI . ) ; consequently the triangle ABC gives AB2 + BC - 2AE2 + 2BE2 ...
Page 84
... parallelogram . In the triangle BFE , the line AC is parallel to the base FE ; hence we have BC : CE : BA : AF ( Prop . XV . ) ; or put- ting CD in the place of its equal AF , BC CE : BA : CD . In the same triangle BEF , CD is parallel ...
... parallelogram . In the triangle BFE , the line AC is parallel to the base FE ; hence we have BC : CE : BA : AF ( Prop . XV . ) ; or put- ting CD in the place of its equal AF , BC CE : BA : CD . In the same triangle BEF , CD is parallel ...
Page 101
... parallelogram , AB its base , DE its alti- tude : between AB and DE find a mean propor- tional XY ; then will the square described upon D A E B XY be equivalent to the parallelogram ABCD . For , by construction , AB XY :: XY : DE ...
... parallelogram , AB its base , DE its alti- tude : between AB and DE find a mean propor- tional XY ; then will the square described upon D A E B XY be equivalent to the parallelogram ABCD . For , by construction , AB XY :: XY : DE ...
Page 112
... parallelogram and even a rhombus , since AB - BC - CO - AO ; hence the sum of the squares of the diagonals AC2 + BO2 is equivalent to the sum of the squares of the sides , that is , to 4AB2 , or 4BO ( Book IV . Prop XIV . Cor . ) : and ...
... parallelogram and even a rhombus , since AB - BC - CO - AO ; hence the sum of the squares of the diagonals AC2 + BO2 is equivalent to the sum of the squares of the sides , that is , to 4AB2 , or 4BO ( Book IV . Prop XIV . Cor . ) : and ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex