The Mathematical Monthly, Հատոր 2John Daniel Runkle John Bartlett, 1860 "A complete catalogue of the writings of Sir John Herschel": v. 3, p. 220-227. |
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A₁ Academy acres Algebra Amherst College Astronomical atmosphere axis b₁ BENJAMIN PEIRCE body centre CHARLES HENRY DAVIS CHAUNCEY WRIGHT circle coefficients College computation Conic Sections cos² curve cyclone denote distance earth's ellipse equal equation force fraction Geometry given gives Hence hyperbola IVISON J. D. RUNKLE logarithms Marietta College Mass Mathematical MATHEMATICAL MONTHLY metic motion multiplied oxen perihelion perpendicular Perry City PHINNEY plane polygon PRIZE PROBLEMS PRIZE SOLUTION Probs Prof Professor proposition Public Instruction Publishers quaternions R₁ radius ratio rhombs right angles Robinson's roots School sides SIMON NEWCOMB sin² SOLUTION OF PROBLEM Spencerian Penmanship spherical square Superintendent of Public supposed surface tangent Theorem tion triangle TRUMAN HENRY SAFFORD vector velocity whole number York
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Էջ 105 - The angles of a triangle cannot be altered without altering the length of the sides. — Proof. If in any triangle, as ABC, the sides were unchangeable, any alteration of the angles A and В would by article 93 make the point С move in two directions at once, (namely, at right angles to AC, and at right angles to В С,) which is impossible, and therefore the angles cannot be altered. 95. Corollary. If the three sides of a triangle are respectively equal to the three sides of another triangle, the...
Էջ 32 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.
Էջ 264 - URIAH A. BOYDEN, ESQ., of Boston, Mass., has deposited with THE FRANKLIN INSTITUTE the sum of one thousand dollars, to be awarded as a premium to "Any resident of North America who shall determine by experiment whether all rays of light,* and other physical rays, are or are not transmitted with the same velocity.
Էջ 34 - The earlier sections of each chapter contain that kind of matter which has usually been thought suitable for the beginner, while the latter ones are devoted either to an account of recent discovery, or...
Էջ 114 - Two circles touch each other externally, the diameter of one being double of the diameter of the other ; through the point of contact any line is drawn to meet the circumferences of both ; shew that the part of the line which lies in the larger circle is double of that in the smaller.
Էջ 32 - On the calculation of the oblateness of the earth, by means of the observed lengths of a pendulum in different latitudes, according to the method given by La Place in the second volume of his " Mecanique Celeste," with remarks on other parts of the same work, relating to the figure of the earth.
Էջ 118 - What fraction is that, to the numerator of which if 1 be added, its value will be |, but if 1 be added to its denominator its value will be i.
Էջ 118 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes f ; but the denominator being doubled, and the numerator increased by 2, the value becomes | ? Ans.
Էջ 133 - Law of cosines for sides: cos a = cos b cos с + sin 6 sin с cos A cos b = cos a cos с + sin a sin с cos ß cos с = cos a cos...
Էջ 71 - Thus, from the self-evident truth of article 78, we find that the product of the means bears the same ratio to the product NXQ that is borne to it by the product of the extremes. And as it is self-evident that two quantities, bearing the same ratio to a third, must be equal to each other, we have proved that the product of the means is equal to that of the extremes. 82. Definition. When both the means are the same quantity, that quantity is called a mean proportional between the extremes. 83. Corollary....