Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 12
... 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 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
... 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 S B coincide with AC ( P. M D IV . ) ; and consequently , they will be equally dis- A K R tant from the ...
... 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 S B coincide with AC ( P. M D IV . ) ; and consequently , they will be equally dis- A K R 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
ABē ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following