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algebraic applied arithmetic Astronomische Nachrichten axes axis base Benjamin Peirce Cambridge centre of similitude Chauncey Wright circumference Coll College comet cone constant coordinates corresponding curve cycloid demonstration denote dial diameter distance divisor draw earth ellipse envelope epicycloid equal equation figure fluid formula four oppositions Geometry given circle gives Guldin height Hence hypocycloid inscribed inscribed sphere intersection Journal length locus Mathematical Monthly Mathematics method miles motion Nautical Almanac nucleus number of positions orbit Pappus parabola parallel perihelion perpendicular plane PRIZE PROBLEMS Prize Solution Prof proposition prove radical axis radius ratio right angles roots rotation Sept sides sin2 slant height solid solid of revolution sphere square straight line Student supposed surface tail tangent theorem Theorem of Pappus tion touch triangle Truman Henry Safford velocity vertex vertical 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 429 - This work is intended to follow the Elements, and gives an extended course in the higher as well as the more rudimental departments of the science, adapted for advanced schools and colleges. It is based on the admirable work of Vincent, revised by Bourdon, which has long been the geometrical standard in the French schools.
Page 429 - This work covers nearly the same ground as the Elementary, differing from it principally in presenting a greater number of examples. It may, therefore, either follow the Elementary, or be substituted for it. IV. HIGHER ARITHMETIC. 12mo. 324 pages. Cloth. Price 75 cents. — This is intended as a finishing book for those who would complete a thorough arithmetical course. Perkins
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 429 - In these Elements it is aimed to strip Geometry of its difficulties, and render it an attractive study. This is effected by giving a practical bearing to every thing that is taught. This original feature invests Geometry with an interest of which its apparently abstract character has heretofore deprived it.
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...
Page 429 - Among the peculiar merits of this work, besides its simplicity, are the conciseness of its rules and definitions ; its close and logical reasoning, which calls the powers of the learner into active exercise ; and the great number and variety of its examples, which afford every opportunity for extended practice.