Elements of Geometry and TrigonometryWiley & Long, 1836 - 359 σελίδες |
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Σελίδα 35
... proportional quantitics , 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 quantitics , 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 ...
Σελίδα 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 ...
Σελίδα 37
... proportional quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be proportional . Let and M : N :: P : Q M : R :: P : S then will N : Q :: R : S For , by alternation M ...
... proportional quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be proportional . Let and M : N :: P : Q M : R :: P : S then will N : Q :: R : S For , by alternation M ...
Σελίδα 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 ...
Σελίδα 39
... proportional quantities , if the two consequents be either augmented or diminished by quantities which have the same ratio as the antecedents , the resulting quantities and the ante- cedents will be proportional . Let For , since And ...
... proportional quantities , if the two consequents be either augmented or diminished by quantities which have the same ratio as the antecedents , the resulting quantities and the ante- cedents will be proportional . Let For , since And ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent altitude angle ACB ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang 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 greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment side BC similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Δημοφιλή αποσπάσματα
Σελίδα 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Σελίδα 18 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 233 - It is, indeed, evident, that the negative characteristic will always be one greater than the number of ciphers between the decimal point and the first significant figure.
Σελίδα 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Σελίδα 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Σελίδα 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Σελίδα 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 159 - S-o6c be the smaller : and suppose Aa to be the altitude of a prism, which having ABC for its base, is equal to their difference. Divide the altitude AT into equal parts Ax, xy, yz, &c. each less than Aa, and let k be one of those parts ; through the points of division...
Σελίδα 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.