Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 46
... taken twice ; that is , to four right angles . If the angles of a quadrilateral are equal , each will be a right angle . Cor . 2. The sum of the interior angles of a pentagon is equal to two right angles taken three times ; that is , to ...
... taken twice ; that is , to four right angles . If the angles of a quadrilateral are equal , each will be a right angle . Cor . 2. The sum of the interior angles of a pentagon is equal to two right angles taken three times ; that is , to ...
Page 47
... taken as many times as the polygon has sides , less two : hence , the sum of the exterior angles is equal to two right angles taken twice ; that is , equal to four right angles ; which was to be proved . PROPOSITION XXVIII . THEOREM ...
... taken as many times as the polygon has sides , less two : hence , the sum of the exterior angles is equal to two right angles taken twice ; that is , equal to four right angles ; which was to be proved . PROPOSITION XXVIII . THEOREM ...
Page 49
... taken at equal distances from a line , and on the same side of it , the line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The diagonals of a parallelogram divide each other into equal parts , or ...
... taken at equal distances from a line , and on the same side of it , the line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The diagonals of a parallelogram divide each other into equal parts , or ...
Page 77
... taken as the measures of the angles . That is , if a circum- ference be described from the vertex of any angle , as a cen- tre , and with a fixed radius , the arc intercepted between the sides of the angle may be taken as the measure of ...
... taken as the measures of the angles . That is , if a circum- ference be described from the vertex of any angle , as a cen- tre , and with a fixed radius , the arc intercepted between the sides of the angle may be taken as the measure of ...
Page 79
... angle DCB by half the arc : D B DAB hence , the two angles , taken together , are mea- sured by half the circumference : hence , their sum is equal to two right angles . PROPOSITION XIX . THEOREM . Any angle formed by two BOOK III . 79.
... angle DCB by half the arc : D B DAB hence , the two angles , taken together , are mea- sured by half the circumference : hence , their sum is equal to two right angles . PROPOSITION XIX . THEOREM . Any angle formed by two BOOK III . 79.
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Common terms and phrases
ABĀ² 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