Elements of Geometry and Trigonometry: With Practical ApplicationsR.S. Davis & Company, 1869 - 382 pages |
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Page 49
... B : D . : : For , since the magnitudes are in proportion , A B = C D B we and multiplying each member of this equation by have C ' AX B = BX C СХВ DX C ' I which , reduced to the lowest terms , gives whence 5 BOOK II . 49.
... B : D . : : For , since the magnitudes are in proportion , A B = C D B we and multiplying each member of this equation by have C ' AX B = BX C СХВ DX C ' I which , reduced to the lowest terms , gives whence 5 BOOK II . 49.
Page 51
... Multiplying each side of this equation by any number , m , we have therefore mXAXB = mxBXA ; ( m x A ) x B = ( m × B ) × A. Hence , by Prop . II . , mXA : m X B :: A : B. PROPOSITION X. - THEOREM . 144. Magnitudes which are proportional ...
... Multiplying each side of this equation by any number , m , we have therefore mXAXB = mxBXA ; ( m x A ) x B = ( m × B ) × A. Hence , by Prop . II . , mXA : m X B :: A : B. PROPOSITION X. - THEOREM . 144. Magnitudes which are proportional ...
Page 53
... Multiplying together the corresponding members of these equations , we have AX DX EXH = BX CXFX G. Hence , by Prop . II . , AXE : BX F :: CxG : D x H. PROPOSITION XIV . - THEOREM . 150. If three magnitudes are proportionals , the first ...
... Multiplying together the corresponding members of these equations , we have AX DX EXH = BX CXFX G. Hence , by Prop . II . , AXE : BX F :: CxG : D x H. PROPOSITION XIV . - THEOREM . 150. If three magnitudes are proportionals , the first ...
Page 81
... multiplied by their altitudes . Let ABCD , AEGF be two rectangles ; then will ABCD be to AEGF as AB multiplied by AD is to AE multiplied by AF . Having placed the two rectangles so that the angles at A are verti- cal , produce the sides ...
... multiplied by their altitudes . Let ABCD , AEGF be two rectangles ; then will ABCD be to AEGF as AB multiplied by AD is to AE multiplied by AF . Having placed the two rectangles so that the angles at A are verti- cal , produce the sides ...
Page 106
... multiplying together the corresponding terms of these proportions , and omitting the common term ABE , we have ( Prop . XIII . Bk . II . ) , ABC : ADE :: ABX AC : ADX AE . 273. Cor . If the rectangles of the sides containing the equal ...
... multiplying together the corresponding terms of these proportions , and omitting the common term ABE , we have ( Prop . XIII . Bk . II . ) , ABC : ADE :: ABX AC : ADX AE . 273. Cor . If the rectangles of the sides containing the equal ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle equal angles ACD base bisect centre chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater GREENLEAF'S half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent triangle ABC triangle equal trigonometric functions TRIGONOMETRY vertex
Popular passages
Page 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 95 - Each side of a spherical triangle is less than the sum of the other two sides.
Page 172 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their common section, will be perpendicular to the other plane.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 272 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 33 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 94 - In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the straight line that joins the middle points of the diagonals.
Page 102 - 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'.