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
... tains the same unit an equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to coincide throughout their whole extent . ELEMENTS OF OF GEOMETRY . BOOK I. BLEMENTARY PRINCIPLES . 12 GEOMETRY .
... tains the same unit an equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to coincide throughout their whole extent . ELEMENTS OF OF GEOMETRY . BOOK I. BLEMENTARY PRINCIPLES . 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
... at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
... at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
Page 67
... placed upon ACH , so that the centre R shall fall upon the centre O , and the point K upon the point A : then will the chord KL coincide with AC ( P. IV . ) ; and consequently , they will be equally dis- tant from the centre ; which was ...
... placed upon ACH , so that the centre R shall fall upon the centre O , and the point K upon the point A : then will the chord KL coincide with AC ( P. IV . ) ; and consequently , they will be equally dis- tant from the centre ; which was ...
Page 75
... then will they be proportional to the arcs AB and FH . For , let the less angle FOH , angle ACB , that it shall C DIOB F be placed upon the greater take the position ACD . Then , it the proposition is not true , let BOOK III . 75.
... then will they be proportional to the arcs AB and FH . For , let the less angle FOH , angle ACB , that it shall C DIOB F be placed upon the greater take the position ACD . Then , it the proposition is not true , let BOOK III . 75.
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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