## An easy introduction to the mathematics: in which the theory and practice are laid down and familiarly explained ... A complete and easy system of elementary instruction in the leading branches of the mathematics; ... Adapted to the use of schools, junior students at the universities, and private learners, especially those who study without a tutor. In two volumes, Volume 2 |

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Algebra arithmetical progression base biquadratic equation bisected called centre chord circle circumference co-secant co-sine co-tangent common compasses Conic Sections conjugate hyperbola contained cube cubic equation curve demonstration described diameter difference distance divided divisors draw drawn ellipse equal equiangular Euclid Euclid's Elements Examples.—1 former fourth geometrical progression Geometry given equation given ratio greater Hence hyperbola infinite series latter latus rectum less likewise logarithms magnitude major axis manner measure method multiplied number of terms odd number ordinate parabola parallel parallelogram perpendicular plane polygon problem prop proportionals proposed proposition Q. E. D. Cor quadrant quotient radius rectangle rectilineal figures right angles rule scale secant shewn sides substituted subtracted tangent theor theorem third unknown quantity versed sine whence wherefore whole numbers

### Popular passages

Page 320 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.

Page 405 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 287 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 66 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 272 - But things which are equal to the same are equal to one another (Ax.

Page 267 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.

Page 263 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

Page 281 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Page 294 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.

Page 190 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of