Elements of Geometry: With Practical Applications to MensurationLeach, Shewell and Sanborn, 1863 - 320 σελίδες |
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Αποτελέσματα 1 - 5 από τα 77.
Σελίδα 49
... ; then will A : C :: B : D. For , since the magnitudes are in proportion , A B = C Ꭰ and multiplying each member of this equation by B C ' we have AX B BX C = СХВ DX C ' which , reduced to the lowest terms , gives A BOOK II . 49.
... ; then will A : C :: B : D. For , since the magnitudes are in proportion , A B = C Ꭰ and multiplying each member of this equation by B C ' we have AX B BX C = СХВ DX C ' which , reduced to the lowest terms , gives A BOOK II . 49.
Σελίδα 51
... Multiplying each side of this equation by any number , m , we have therefore mxAX Bmx BX A ; ( m x A ) X B = ( m × B ) × A. Hence , by Prop . II . , mx A : m X B :: A : B. PROPOSITION X. THEOREM . - 144. Magnitudes which are ...
... Multiplying each side of this equation by any number , m , we have therefore mxAX Bmx BX A ; ( m x A ) X B = ( m × B ) × A. Hence , by Prop . II . , mx A : m X B :: A : B. PROPOSITION X. THEOREM . - 144. Magnitudes which are ...
Σελίδα 53
... Multiplying together the corresponding members of these equations , we have AX DX EX HBX CXFX G. Hence , by Prop . II . , AXE : BX F :: CX G : DX H. PROPOSITION XIV . THEOREM . - 150. If three magnitudes are proportionals , the first ...
... Multiplying together the corresponding members of these equations , we have AX DX EX HBX CXFX G. Hence , by Prop . II . , AXE : BX F :: CX G : DX H. PROPOSITION XIV . THEOREM . - 150. If three magnitudes are proportionals , the first ...
Σελίδα 81
... multiplied by their altitudes . E H D C G F B A Let ABCD , AEGF be two rectangles ; then will ABCD be to AEGF as A B multiplied by AD is to AE multiplied by A F. Having placed the two rectangles so that the angles at A are verti- cal ...
... multiplied by their altitudes . E H D C G F B A Let ABCD , AEGF be two rectangles ; then will ABCD be to AEGF as A B multiplied by AD is to AE multiplied by A F. Having placed the two rectangles so that the angles at A are verti- cal ...
Σελίδα 106
... multiplying together the corresponding terms of these proportions , and omitting the common term A BE , we have ( Prop . XIII . Bk . II . ) , ABC : ADE :: ABX AC : ADXA E. 273. Cor . If the rectangles of the sides containing the equal ...
... multiplying together the corresponding terms of these proportions , and omitting the common term A BE , we have ( Prop . XIII . Bk . II . ) , ABC : ADE :: ABX AC : ADXA E. 273. Cor . If the rectangles of the sides containing the equal ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: With Practical Applications to Mensuration Benjamin Greenleaf Πλήρης προβολή - 1874 |
Elements of Geometry: With Practical Application to Mensuration Benjamin Greenleaf Πλήρης προβολή - 1869 |
Elements of Geometry: With Practical Applications to Mensuration Benjamin Greenleaf Πλήρης προβολή - 1872 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C ABCD adjacent angles altitude angle equal base bisect 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 formulæ frustum gles greater 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 Required the area 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 THEOREM triangle ABC triangle equal trigonometric functions vertex
Δημοφιλή αποσπάσματα
Σελίδα 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 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.
Σελίδα 120 - At a point in a given straight line to make an angle equal to a given angle.
Σελίδα 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Σελίδα 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Σελίδα 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Σελίδα 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.
Σελίδα 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.
Σελίδα 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Σελίδα 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.