Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 34
Page 50
... ratio to the second , that the second has to the third ; and then the middle term is said to be a mean proportional between the other two . 9. Magnitudes are in proportion by alternation , or alter- nately , when antecedent is compared ...
... ratio to the second , that the second has to the third ; and then the middle term is said to be a mean proportional between the other two . 9. Magnitudes are in proportion by alternation , or alter- nately , when antecedent is compared ...
Page 51
... ratio which M has to N , let P have to Q ' , ( a number greater or less than Q , ) the same ratio which M has to N : that is , let M : N :: P : Q : M × Q ' = N × P ; then ( P. 1 ) , NXP hence , Q ' = NXP ; but , Q = M M Consequently , Q ...
... ratio which M has to N , let P have to Q ' , ( a number greater or less than Q , ) the same ratio which M has to N : that is , let M : N :: P : Q : M × Q ' = N × P ; then ( P. 1 ) , NXP hence , Q ' = NXP ; but , Q = M M Consequently , Q ...
Page 52
... ratio of an antecedent and consequent of the one is equal to the ratio of an antecedent and consequent of the other , the remaining terms will be proportional . For , if we had the two proportions , M : P :: N : Q and R : S :: T : V ...
... ratio of an antecedent and consequent of the one is equal to the ratio of an antecedent and consequent of the other , the remaining terms will be proportional . For , if we had the two proportions , M : P :: N : Q and R : S :: T : V ...
Page 53
... magnitudes , have the same ratio as the magnitudes themselves . Let M and N be any two magnitudes , and m any num- ber whatever ; then will m × M , and m × N , be equal mul- tiples of M and N : and m × M BOOK II : 53.
... magnitudes , have the same ratio as the magnitudes themselves . Let M and N be any two magnitudes , and m any num- ber whatever ; then will m × M , and m × N , be equal mul- tiples of M and N : and m × M BOOK II : 53.
Page 54
... ratio of M to N. For , MXN = NXM : multiplying each member by m , and we have mxMxN = mxNX M : then ( P. 2 ) , mxM : mxN :: M : N. PROPOSITION VIII . THEOREM . Of four proportional magnitudes , if there be taken any equimul- tiples of ...
... ratio of M to N. For , MXN = NXM : multiplying each member by m , and we have mxMxN = mxNX M : then ( P. 2 ) , mxM : mxN :: M : N. PROPOSITION VIII . THEOREM . Of four proportional magnitudes , if there be taken any equimul- tiples of ...
Other editions - View all
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...