Elements of Geometry: With Practical Applications to MensurationLeach, Shewell and Sanborn, 1863 - 320 σελίδες |
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Αποτελέσματα 1 - 5 από τα 51.
Σελίδα 46
... PROPORTIONAL between the extremes ; and if , in a series of proportional magnitudes , each consequent is the same as the next antecedent , those magnitudes are said to be in cONTINUED PROPORTION . Thus , if we have A : B :: B : C :: C ...
... PROPORTIONAL between the extremes ; and if , in a series of proportional magnitudes , each consequent is the same as the next antecedent , those magnitudes are said to be in cONTINUED PROPORTION . Thus , if we have A : B :: B : C :: C ...
Σελίδα 49
... proportional between the other two . Let AXC tween A and C. B2 ; then B is a mean proportional be- For , dividing each member of the given equation by BX C , we have whence A = B B C A : B :: B : C. PROPOSITION V. - THEOREM . 139. If ...
... proportional between the other two . Let AXC tween A and C. B2 ; then B is a mean proportional be- For , dividing each member of the given equation by BX C , we have whence A = B B C A : B :: B : C. PROPOSITION V. - THEOREM . 139. If ...
Σελίδα 51
... proportional to the sam proportionals , will be proportional to each other . Let A B E F , and C : D :: E : F ; then will : A : B :: C : D. For , by the given proportions , we have A E = B F ' E с and = D F Therefore , it is evident ...
... proportional to the sam proportionals , will be proportional to each other . Let A B E F , and C : D :: E : F ; then will : A : B :: C : D. For , by the given proportions , we have A E = B F ' E с and = D F Therefore , it is evident ...
Σελίδα 52
... proportional , any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents . Let AB :: C : D :: E : F ; then will A : B :: A + C + E : B + D + F. For , from the given proportion , we have ...
... proportional , any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents . Let AB :: C : D :: E : F ; then will A : B :: A + C + E : B + D + F. For , from the given proportion , we have ...
Σελίδα 53
... proportional magnitudes , the products of the corresponding terms will be propor- tionals . Let A B C : D , and E : F :: G : H ; then will : AXE : BX F :: CX G : DX H. For , from the first of the given proportions , by Prop . I. , we ...
... proportional magnitudes , the products of the corresponding terms will be propor- tionals . Let A B C : D , and E : F :: G : H ; then will : AXE : BX F :: CX G : DX H. For , from the first of the given proportions , by Prop . I. , we ...
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 ACB angle equal arc A B 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 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 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 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.