Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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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 ...
... 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 ...
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 mains , re- ACD ECB . E B In like manner , we find , ACD + ACE ACD + DCB ; 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 mains , re- ACD ECB . E B In like manner , we find , ACD + ACE ACD + DCB ; 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 . Between A and B they must E A- B C -D coincide ( A ...
... 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 . Between A and B they must E A- B C -D coincide ( A ...
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 AC² adjacent angles altitude angle ACB 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 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 mean proportional 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 six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence