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a₁ algebraic application ARITHMETIC axis BENJAMIN PEIRCE Calculus Cambridge centre CHAUNCEY WRIGHT circumference coefficients Coll College comet cone co÷rdinates cos▓ curve cycloid D₂ demonstration denote derivatives diameter distance divided divisor earth ellipse envelope equal equation figure fluid formula fractions Geometry gives Harvard College Hence hypocycloid inscribed JOSEPH WINLOCK Journal least common multiple Mathematical Mathematical Monthly method miles motion multiplied nucleus number of positions opposite orbit parabola parallel perihelion perpendicular plane poles PRIZE PROBLEMS PRIZE SOLUTION Prof Professor proposition r₁ radical axis radius ratio right angles roots sections sides SIMON NEWCOMB sin▓ solid sphere square straight line student suppose tail tangent theorem tion Treatise triangle TRUMAN HENRY SAFFORD velocity vertex vertical volume whole number
Page 252 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 253 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc. 32. 1.) may be demonstrated, either in common language, or by means of the signs used in algebra. Let the side AB, of the triangle ABC, (Fig. 1.) be continued to D ; let the line BE be parallel to AC; and let GHI be a right angle.
Page 190 - The latitude of the Cambridge Observatory, in Massachusetts, determined from Transits of Stars over the Prime Vertical observed during the months of December, 1844, and January 1845, by Wm.
Page 150 - C., and LUNGE, G. Handbook of Technical Gas-Analysis. With figures and diagrams. Second English edition. Translated from the third greatly enlarged German edition, with some additions by George Lunge, Ph.D.
Page 67 - Traces of a tail were noticed on the 20th of August, and on the 29th it was seen with the naked eye as a hazy star. For a few weeks it occupied a position in the heavens where it rose before the sun and set after it, becoming thus a conspicuous object both in the morning and evening sky. This circumstance gave rise to the erroneous notion that two different comets had appeared. The statement, which was widely circulated, that this was the return of the comet of 1264 and of 1556, supposed by some...