Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page ii
... COMMON SCHOOL COURSE Davies ' Primary Arithmetic . - The fundamental principles displayed in Object Lessons . Davies ' Intellectual Arithmetic . - Referring all operations to the unit 1 as the only tangible basis for logical development ...
... COMMON SCHOOL COURSE Davies ' Primary Arithmetic . - The fundamental principles displayed in Object Lessons . Davies ' Intellectual Arithmetic . - Referring all operations to the unit 1 as the only tangible basis for logical development ...
Page 14
... common point A , is called the ver- -B tex . An angle is designated by naming its sides , or some- times by simply naming its vertex ; thus , the above is called the angle BAC , or simply , the angle A. 11. When one straight line meets ...
... common point A , is called the ver- -B tex . An angle is designated by naming its sides , or some- times by simply naming its vertex ; thus , the above is called the angle BAC , or simply , the angle A. 11. When one straight line meets ...
Page 22
... common A angle ACE ( A. 3 ) , there re- mains , ACD ECB . D In like manner , we find , ACD + ACE ACD + DCB ; E B and , taking away the common angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the ...
... common A angle ACE ( A. 3 ) , there re- mains , ACD ECB . D In like manner , we find , ACD + ACE ACD + DCB ; E B and , taking away the common angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the ...
Page 23
... common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines coincide throughout . E A B -D Between A and B they must coincide ( A. 11 ) ...
... common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines coincide throughout . E A B -D Between A and B they must coincide ( A. 11 ) ...
Page 24
... common angle DCA , there re- mains , DCB DCE , which is impossible , since a part cannot be equal to the whole ( A. 8 ) . Hence , CB must be the prolongation of AC ; which was to be proved . PROPOSITION V. THEOREM . If two triangles ...
... common angle DCA , there re- mains , DCB DCE , which is impossible , since a part cannot be equal to the whole ( A. 8 ) . Hence , CB must be the prolongation of AC ; which was to be proved . PROPOSITION V. THEOREM . If two triangles ...
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Common terms and phrases
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
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 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.
Page 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.
Page 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.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 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.
Page 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 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.
Page 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.