Elements of Geometry and Trigonometry: From the Works of A.M. LegendreA.S. Barnes, 1874 - 455 Seiten |
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Seite 28
... B4 G A E D GI + IC > GC , and BI + IA > AB ; whence , by addition , recollecting that the sum of BI and IC is equal to BC , and the sum of GI and IA , to GA , we have , AG + BC > AB + GC . Or , since AG = AB , and GC = 28 GEOMETRY .
... B4 G A E D GI + IC > GC , and BI + IA > AB ; whence , by addition , recollecting that the sum of BI and IC is equal to BC , and the sum of GI and IA , to GA , we have , AG + BC > AB + GC . Or , since AG = AB , and GC = 28 GEOMETRY .
Seite 52
... whence , A = a ; clearing of fractions , we have , BC = AD ;、 which was to be proved . Cor . If B is equal to C , there will be but three pro- portional quantities ; in this case , the square of the mean is equal to the product of the ...
... whence , A = a ; clearing of fractions , we have , BC = AD ;、 which was to be proved . Cor . If B is equal to C , there will be but three pro- portional quantities ; in this case , the square of the mean is equal to the product of the ...
Seite 54
... whence , B D = · A If we take the reciprocals of both members ( A. 7 ) , we have , A C = ; whence , B : A B Ꭰ which was to be proved . • • D : C ; PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in pro ...
... whence , B D = · A If we take the reciprocals of both members ( A. 7 ) , we have , A C = ; whence , B : A B Ꭰ which was to be proved . • • D : C ; PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in pro ...
Seite 55
... whence , = Α C If we multiply both terms of the first member by m , and both terms of the second member by n , we shall have , mB nD n C ; whence , mA : mB :: nC : nD ; MA = which was to be proved . PROPOSITION IX . THEOREM . If two ...
... whence , = Α C If we multiply both terms of the first member by m , and both terms of the second member by n , we shall have , mB nD n C ; whence , mA : mB :: nC : nD ; MA = which was to be proved . PROPOSITION IX . THEOREM . If two ...
Seite 57
... whence , BA = AB ; - Α ; whence , BC = AD ; F ; whence , BE AF ; ; whence , BG = AH ; & c . A = E Α B 314 Α = & c . , H G Adding and factoring , we have , B ( A + C + E + G + & c . ) = A ( B + D + F + H + & c . ) : hence , from ...
... whence , BA = AB ; - Α ; whence , BC = AD ; F ; whence , BE AF ; ; whence , BG = AH ; & c . A = E Α B 314 Α = & c . , H G Adding and factoring , we have , B ( A + C + E + G + & c . ) = A ( B + D + F + H + & c . ) : hence , from ...
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Häufige Begriffe und Wortgruppen
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Beliebte Passagen
Seite 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Seite 59 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Seite 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Seite 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Seite 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 28 - If two triangles have two sides of the one equal to two sides of the...
Seite 46 - 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 99 - The area of a parallelogram is equal to the product of its base and altitude.
Seite 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Seite 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.