Elements of Geometry and Trigonometry |
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Page 39
... Hence , AB and CD are perpendicular to the same straight line ; hence , they are parallel ( P. 18 ) . PROPOSITION XXIII . THEOREM . Two parallels are everywhere equally distant . Let CD and AB be two parallel straight lines . Through ...
... Hence , AB and CD are perpendicular to the same straight line ; hence , they are parallel ( P. 18 ) . PROPOSITION XXIII . THEOREM . Two parallels are everywhere equally distant . Let CD and AB be two parallel straight lines . Through ...
Page 42
... hence , if all the angles of a quadrilateral are equal , each of them will be a right angle . Hence , each of the angles of a rectangle , and of a square , is a right angle ( D. 25 ) . Cor . 2. The sum of the interior angles of a ...
... hence , if all the angles of a quadrilateral are equal , each of them will be a right angle . Hence , each of the angles of a rectangle , and of a square , is a right angle ( D. 25 ) . Cor . 2. The sum of the interior angles of a ...
Page 49
... hence , their ratio in numbers . Suppose , for instance , we find GB to be contained exactly twice in FD ; BG will be the common measure of the two proposed lines . Put BG = 1 ; we shall then have , FD - 2 ; but EB contains FD once ...
... hence , their ratio in numbers . Suppose , for instance , we find GB to be contained exactly twice in FD ; BG will be the common measure of the two proposed lines . Put BG = 1 ; we shall then have , FD - 2 ; but EB contains FD once ...
Page 52
... hence , M : P :: N : Q PROPOSITION IV . THEOREM . If there be four proportional magnitudes , and four other pro- portional magnitudes , having the antecedents the sume in both , the consequents will be proportional . and Let M : N ...
... hence , M : P :: N : Q PROPOSITION IV . THEOREM . If there be four proportional magnitudes , and four other pro- portional magnitudes , having the antecedents the sume in both , the consequents will be proportional . and Let M : N ...
Page 54
... hence , :: NP : Q2 MxQ = NxP ; m x Mx n x Q = n × N × m × P , by multiplying both members of the equation by mXn . But m XM and n XQ , may be regarded as the two extremes , and n × N and m XP , as the means of a proportion ; hence , mx ...
... hence , :: NP : Q2 MxQ = NxP ; m x Mx n x Q = n × N × m × P , by multiplying both members of the equation by mXn . But m XM and n XQ , may be regarded as the two extremes , and n × N and m XP , as the means of a proportion ; hence , mx ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
adjacent angles altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² Cosine Cosine D Cotang cylinder diagonal diameter distance divided draw drawn equations equivalent feet figure find the area frustum given angle given line gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices ΙΟ
Popular passages
Page 24 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Page 38 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 43 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the sum of the exterior angles.
Page 215 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 93 - The area of a parallelogram is equal to the product of its base and altitude.
Page 231 - The angles of spherical triangles may be compared together, by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle.
Page 232 - F, be respectively poles of the sides BC, AC, AB. For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...