Elements of Geometry and TrigonometryWiley & Long, 1836 - 359 Seiten |
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Seite 53
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
Seite 68
... similar figures , are called homologous sides or angles . 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc ...
... similar figures , are called homologous sides or angles . 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc ...
Seite 73
... similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that of the rectangles , agreeably to the proposition just demonstrated . For ...
... similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that of the rectangles , agreeably to the proposition just demonstrated . For ...
Seite 84
... similar when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED , are two similar figures . Cor . For the similarity of two triangles ...
... similar when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED , are two similar figures . Cor . For the similarity of two triangles ...
Seite 85
... similar . In the two triangles BAC , DEF , suppose we have BC : FF :: AB : DE :: AC : DF ; then will the triangles ABC , DEF have their an- gles_equal , namely , A = D , B = E , C = F . A E 44 B At the point E , make the angle FEG = B ...
... similar . In the two triangles BAC , DEF , suppose we have BC : FF :: AB : DE :: AC : DF ; then will the triangles ABC , DEF have their an- gles_equal , namely , A = D , B = E , C = F . A E 44 B At the point E , make the angle FEG = B ...
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adjacent altitude angle ACB 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 greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM 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
Beliebte Passagen
Seite 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.
Seite 18 - If two triangles have two sides of the one equal to two sides of the...
Seite 233 - It is, indeed, evident, that the negative characteristic will always be one greater than the number of ciphers between the decimal point and the first significant figure.
Seite 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.
Seite 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.
Seite 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Seite 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Seite 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'.
Seite 159 - S-o6c be the smaller : and suppose Aa to be the altitude of a prism, which having ABC for its base, is equal to their difference. Divide the altitude AT into equal parts Ax, xy, yz, &c. each less than Aa, and let k be one of those parts ; through the points of division...
Seite 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.