Elements of Geometry and Trigonometry |
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Page 12
... placed as to coincide throughout their whole extent : they are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the reverse order . ELEMENTS OF GEOMETRY ...
... placed as to coincide throughout their whole extent : they are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the reverse order . ELEMENTS OF 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
... is at 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 .
... is at 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
Adrien Marie Legendre. For , let the circle KLG be placed upon ACH , so that the centre R shall fall upon the centre 0 , and ... placed , that they coincide in all their parts . PROPOSITION IX . THEOREM . If a straight line is BOOK II1 . 67.
Adrien Marie Legendre. For , let the circle KLG be placed upon ACH , so that the centre R shall fall upon the centre 0 , and ... placed , that they coincide in all their parts . PROPOSITION IX . THEOREM . If a straight line is BOOK II1 . 67.
Page 75
... : then will they be proportional to the arcs AB and FH . A DIO BF For , let the less angle FOH , be placed upon the greater angle ACB , 80 that it shall take the position ACD . Then , if the proposition is not true , let BOOK III . 75.
... : then will they be proportional to the arcs AB and FH . A DIO BF For , let the less angle FOH , be placed upon the greater angle ACB , 80 that it shall take the position ACD . Then , if the proposition is not true , let BOOK III . 75.
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Common terms and phrases
ABCD ACĀ² 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 line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence