Elements of Geometry and Trigonometry |
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Page 35
... proportional quantities , the first and third are called the antecedents , and the second and fourth the conse- quents ; and the last is said to be a fourth proportional to the other three taken in order . 4. Three quantities are in ...
... proportional quantities , the first and third are called the antecedents , and the second and fourth the conse- quents ; and the last is said to be a fourth proportional to the other three taken in order . 4. Three quantities are in ...
Page 36
... proportional quantities ( Def . 4. ) , the product of the extremes will be equal to the square of the mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will ...
... proportional quantities ( Def . 4. ) , the product of the extremes will be equal to the square of the mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will ...
Page 37
Adrien Marie Legendre. PROPOSITION IV . THEOREM . If there be four proportional quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be proportional . Let M : N :: P : Q ...
Adrien Marie Legendre. PROPOSITION IV . THEOREM . If there be four proportional quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be proportional . Let M : N :: P : Q ...
Page 38
... proportional quantities , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of the two consequents , the four resulting quantities will be proportional . Let M , N , P , Q , be the numerical ...
... proportional quantities , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of the two consequents , the four resulting quantities will be proportional . Let M , N , P , Q , be the numerical ...
Page 39
... proportional . Let For , since And since Therefore , or , hence M : NP : Q , and let also M : P :: m : n , then will M : Р : : N ± m : Q ± n . M : NP : Q , M × Q = NxP . M : P :: m : n , Mxn = Pxm MxQMxn = NxP ± Pxm Mx ( Q ± n ) = P ...
... proportional . Let For , since And since Therefore , or , hence M : NP : Q , and let also M : P :: m : n , then will M : Р : : N ± m : Q ± n . M : NP : Q , M × Q = NxP . M : P :: m : n , Mxn = Pxm MxQMxn = NxP ± Pxm Mx ( Q ± n ) = P ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex