Elements of Geometry and Trigonometry |
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Page 83
... give AB - AD : AD :: AC — AE : AE , or BD : AD :: CĚ : AE . PROPOSITION XVII . THEOREM . The line which bisects the vertical angle of a triangle , divides the base into two segments , which are proportional to the adjacent sides . In ...
... give AB - AD : AD :: AC — AE : AE , or BD : AD :: CĚ : AE . PROPOSITION XVII . THEOREM . The line which bisects the vertical angle of a triangle , divides the base into two segments , which are proportional to the adjacent sides . In ...
Page 92
... give the angles , ABC = FGH , BCA = GHF , ACD = FÍI : hence BCD = GHI , likewise CDE = HIK , & c . Moreover we shall have AB : FG BC : GH : AC : FH :: CD : HI , & c .; hence the two polygons have their angles equal and their sides pro ...
... give the angles , ABC = FGH , BCA = GHF , ACD = FÍI : hence BCD = GHI , likewise CDE = HIK , & c . Moreover we shall have AB : FG BC : GH : AC : FH :: CD : HI , & c .; hence the two polygons have their angles equal and their sides pro ...
Page 94
... give the proportion AO : DO :: CO : OB . A B Cor . Therefore AO.OB DO.CO : hence the rectangle under the two segments of the one chord is equal to the rect- angle under the two segments of the other . PROPOSITION XXIX . THEOREM . If ...
... give the proportion AO : DO :: CO : OB . A B Cor . Therefore AO.OB DO.CO : hence the rectangle under the two segments of the one chord is equal to the rect- angle under the two segments of the other . PROPOSITION XXIX . THEOREM . If ...
Page 95
... gives OA = OC.OD . AO . PROPOSITION XXXI . THEOREM . · If either angle of a triangle be bisected by a line terminating ... give the proportion BA : AE : : AD : AC ; hence BA.AC-AE.AD ; but AE - AD + DE , and multi- plying each of these ...
... gives OA = OC.OD . AO . PROPOSITION XXXI . THEOREM . · If either angle of a triangle be bisected by a line terminating ... give the proportion BA : AE : : AD : AC ; hence BA.AC-AE.AD ; but AE - AD + DE , and multi- plying each of these ...
Page 96
... give the proportion AB CE : AD : AC ; and hence AB.AC-CE.AD . B Cor . If these equal quantities be multiplied by the same quantity BC , there will result AB.AC.BC = CE.AD.BC ; now AD.BC is double of the area of the triangle ( Prop . VI ...
... give the proportion AB CE : AD : AC ; and hence AB.AC-CE.AD . B Cor . If these equal quantities be multiplied by the same quantity BC , there will result AB.AC.BC = CE.AD.BC ; now AD.BC is double of the area of the triangle ( Prop . VI ...
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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