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 12
... are equal , when they are equal in measure , When they may be so placed as to coincide through- out their whole extent , they are equal in all their parts . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
... are equal , when they are equal in measure , When they may be so placed as to coincide through- out their whole extent , they are equal in all their parts . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
Page 63
... placed upon the sector EOG , so that the angle ACD shall coincide with the angle EOG , the sectors will coincide throughout ; and , consequently , the arcs AMD and ENG will coincide : hence , they will be equal ; which was to be proved ...
... placed upon the sector EOG , so that the angle ACD shall coincide with the angle EOG , the sectors will coincide throughout ; and , consequently , the arcs AMD and ENG will coincide : hence , they will be equal ; which was to be proved ...
Page 66
... from the centre . 1o . In the equal circles chords AC and KL be distant from the centres . ACH ACH and KLG , and KLG , let the equal : then will they be equally For , let the circle KLG be placed upon the 66 GEOMETRY .
... from the centre . 1o . In the equal circles chords AC and KL be distant from the centres . ACH ACH and KLG , and KLG , let the equal : then will they be equally For , let the circle KLG be placed upon the 66 GEOMETRY .
Page 67
... placed upon the centre R shall fall upon the centre O , K upon the point A : then will the chord coincide with AC ( P. IV . ) ; and consequently , KL ACH , so that and the point S B M ED A K R they will be equally dis- tant from the ...
... placed upon the centre R shall fall upon the centre O , K upon the point A : then will the chord coincide with AC ( P. IV . ) ; and consequently , KL ACH , so that and the point S B M ED A K R they will be equally dis- tant from the ...
Page 75
... then will they be proportional to the arcs AB and FH . A DIOB F BF For , let the less angle FOH , be placed upon the greater angle ACB , SO that it shall take the position ACD . Then , if the proposition is not true , let BOOK II . 75.
... then will they be proportional to the arcs AB and FH . A DIOB F BF For , let the less angle FOH , be placed upon the greater angle ACB , SO that it shall take the position ACD . Then , if the proposition is not true , let BOOK II . 75.
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence