Elements of Geometry and Trigonometry |
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Page 83
... give AB — AD : AD : : AC — AE : AE , or BD : AD :: CE : 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 :: CE : 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 = FHI : 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 ...
... give the angles , ABC = FGH , BCA = GHF , ACD = FHI : 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 ...
Page 94
... give the proportion AO : DO : CO : OB . B Cor . Therefore AO.OB DO.CO : hence the rectangle ander the two segments of the one chord is equal to the rect- angle under the two segments of the other . PROPOSITION XXIX . THEOREM . If from ...
... give the proportion AO : DO : CO : OB . B Cor . Therefore AO.OB DO.CO : hence the rectangle ander the two segments of the one chord is equal to the rect- angle under the two segments of the other . PROPOSITION XXIX . THEOREM . If from ...
Page 95
... gives OA - OC.OD . PROPOSITION XXXI . THEOREM . If either angle of a triangle be bisected by a line terminating in the ... 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 . PROPOSITION XXXI . THEOREM . If either angle of a triangle be bisected by a line terminating in the ... 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 . 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 . 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 altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment side BC similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.