Elements of Geometry: With Practical Applications to MensurationLeach, Shewell and Sanborn, 1863 - 320 Seiten |
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Seite 11
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel . 26. A RECTANGLE is any parallel- ogram whose angles are right angles ; as the parallelogram A B C D. D C A B A SQUARE is a rectangle whose sides are equal ; BOOK I.
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel . 26. A RECTANGLE is any parallel- ogram whose angles are right angles ; as the parallelogram A B C D. D C A B A SQUARE is a rectangle whose sides are equal ; BOOK I.
Seite 12
With Practical Applications to Mensuration Benjamin Greenleaf. A SQUARE is a rectangle whose sides are equal ; as the rectangle EFGH . 27. A RHOMBOID is any parallelo- gram whose angles are not right an- gles ; as the parallelogram IJKL ...
With Practical Applications to Mensuration Benjamin Greenleaf. A SQUARE is a rectangle whose sides are equal ; as the rectangle EFGH . 27. A RHOMBOID is any parallelo- gram whose angles are not right an- gles ; as the parallelogram IJKL ...
Seite 48
... square of the mean . Let A B B : C ; then will A X C = B2 . For , since the magnitudes are in proportion , A B = B C ' and , by Prop . I. , AX CBX B , or AX C = B2 . PROPOSITION IV . - THEOREM . 138. If the product 48 ELEMENTS OF GEOMETRY .
... square of the mean . Let A B B : C ; then will A X C = B2 . For , since the magnitudes are in proportion , A B = B C ' and , by Prop . I. , AX CBX B , or AX C = B2 . PROPOSITION IV . - THEOREM . 138. If the product 48 ELEMENTS OF GEOMETRY .
Seite 49
... square of a third , the third is a mean 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 ...
... square of a third , the third is a mean 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 ...
Seite 53
... square of the first is to the square of the second . Let A B B : C ; then will A : C :: A2 : B2 . : For , from the given proportion , by Prop . III . , we have AXC B2 . = Multiplying each side of this equation by A gives A2 × CA X B2 ...
... square of the first is to the square of the second . Let A B B : C ; then will A : C :: A2 : B2 . : For , from the given proportion , by Prop . III . , we have AXC B2 . = Multiplying each side of this equation by A gives A2 × CA X B2 ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 120 - At a point in a given straight line to make an angle equal to a given angle.
Seite 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.
Seite 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.