est? What is discount? In interest, what is rate? What is the principal? What is the amount? What is the general rule for sim. ple interest? What is compound interest? What is the rule? What is the common rule for calculating interest on notes when there are endorsements? What is the Massachusetts rule? What is the Connecticut rule? What is ratio? How may the ratio between two quantities be represented? What is the consequent? What the antecedent? What is proportion? What is direct proportion? What is inverse proportion? In each case, how is the fourth term found? What is compound proportion? How many terms are there given in compound proportion? How is the sixth found? What is involution? What are powers? What is the index? What is evolution? What does a root take its name from? What is the rule for extracting the square root? What is the rule for extracting the cube root? What is arithmetical progression? How may the sum of all the terms be found? How may the common difference of the terms be found? How may the number of terms be found? What is geometrical progression? How may the sum of the terms be found? How is the last term found? What is alligation? is an annuity? What is permutation of quantities? ALGEBRA. What What is algebra ? What are some of the advantages of algebra over common arithmetic? What is a simple quantity? What is a compound quantity? What is a binomial? What is the reciprocal of a quantity? When is one quantity a multiple of another? When is one quantity the measure of another? What is a negative quantity? What is an axiom? What is addition? How are quantities added? How are several terms reduced to one, when the quantities are alike and the signs alike ?-When the given quantities are alike, but the sigus unlike? What is subtraction? How is it performed? What is multiplying by a whole number?-by a fraction? What relation has multiplication by a negative quantity to multipli. cation by a positiye quantity? When the letters have numerical coefficients, what must be done with them? If the signs of the fac tors are alike what will be the sign of the product ?—what if unlike ? What is the general rule for multiplication? What is division? What is the rule in division in regard to signs? When the divisor is found as a factor, how is the division performed? If the letters in the divisor are not to be found in the dividend, how may the division be expressed? In fractions, if the denominator remains the same, how will multiplying the numerator affect the value of the fraction? If the numerator remains the same, what will be the effect of multiplying the denominator? If both numerator and denominator be multiplied or divided by the same quantity, how will the value of the fraction be affected? What changes in the signs will alter the value of the fraction? What changes will not alter its value? How may a fraction be reduced to lower terms? How may fractions of different denominators be reduced to a common denominator? How is an improper fraction reduced to a mixed quantity? How may frac tions be added? How subtracted? How multiplied? How is a fraction multiplied into a quantity equal to its denominator? What is reducing a compound fraction to a simple one the same as? How is one fraction divided by another? What is the reciprocal of a fraction? What is an equation? In what does the reduction of an equation consist? When known and unknown quantities are connected by plus or minus, how is the equation reduced? How, when the unknown quantity is divided by a known quantity? How is an equation cleared of fractions? When the unknown quantity is multiplied into any known quantity, how is the equation reduced? How may a proportion be converted into an equation? How an equation into a proportion? What is a power? What does a coefficient show ?-what an exponent? What is the rule for involv. ing a quantity? What is the power of the product of several factors equal ito? What is the square of a binomial, the terms of which are both positive ?-of a residual? When the root is positive what is the sign of its powers ?-what when negative? How is a quantity which is already a power involved? How is a fraction involved? How may powers be added? How is subtraction of powers performed? How may powers be multiplied? How may powers of the same root be multiplied? What is the product of the sum and difference of two quantities equal to? How may powers be divided? How may a power be divided by another power of the same root? What is a root of a quantity? How may roots be multipli. ed? How is evolution performed? What sign has an odd root of any quantity? What is an even root of an affirmative quantity? What is said of an even root of a negative quantity? How is a binomial or residual square root extracted? What is a surd? How is a rational quantity reduced to the form of a radical? How are quantities of different indices reduced to others of the same value having a common index? How is a part of a root removed from under the radical sign? How may radical quantities be added? When the quantities to be added have the same radical part under the same rational part, how is the addition to be performed? How are radical quantities subtracted? How may quantities under the same radical sign or index be multiplied?-how divided? How is a root divided by another root of the same letter or quantity? When rad. ical quantities which are reduced to the same index have rational co. effiients, how may the rational parts be divided? How are radical quantities involved? How is a root raised to a power of the same naine? When the unknown quantity is under the radical sign, how is the question reduced?-how when the expression containing the unknown quantity is a power? In what manner are equations divided into classes? What is an equation of the first degree ?—of the second degree? What are pure, and what affected equations? In an affected quadratic equation, how is the square completed? After the square is completed, how is the equation reduced? What is a second mode of completing the square? When is an equation said to be independent ?-when dependent? How is one of two unknown quantities exterminated? When there are three unknown quantities how is the equation reduced? What is four times the product of any two numbers equal to ?-the sum of the squares of any two num bers?-half the difference of any two quantities added to half their sum? What is arithmetical ratio ? What is geometrical ratio? What is inverse or reciprocal ratio? What is compound ratio? When is the ratio of the first antecedent to the last consequent equal to that which is compounded of all the intervening ratios? What is the square of a simple ratio called? What is the cube of a simple ratio? What effect has multiplying the antecedent of a couplet by any quantity, on the ratio? and multiplying the consequent? What —multiplying the consequent, and what dividing the consequent ? If the antecedent and consequent be both multiplied or both divided by the same quantity, how will the ratio be affected? What is the ratio of two fractions which have a common denominator? What is the direct ratio of two fractions which have a common numerator? How is a ratio of greater inequality affected by being compounded with another ratio? How-the ratio of lesser inequality? If, in several couplets the ratios are equal, what ratio has the sum of all the antecedents to the sum of all the consequents? How is a ratio of greater inequality affected by adding the same quantity to both terms? How--a ratio of lesser inequality? What is proportion? Of how many kinds? What are homologous terms? What analogous terms? What is inverse or reciprocal proportion? When is the sum of the extremes double the mean? When is the product of the extremes equal to the product of the means? How is a mean proportional between two quantities found? What six changes can be made in a proportion without destroying it? When are all the ratios equal? What is harmonical or musical proportion? When does one quantity vary directly as another? When--inversely? When-as two others jointly? When does one quantity vary directly as a second, and inversely as a third? When is the quotient of one quantity divided by another, constant? If the product of two quantities is constant, how does one vary in respect to the other? Can a factor in one term be transferred so as to become a divisor in another? If two quantities vary respectively as a third, how do they vary in respect to each other? If two quantities vary respectively as a third, how will their sum or difference vary? If the square of the sum of two quantities varies as the square of their difference, how will the sum of their squares vary in respect to their product? If any quantity vary as another, how will any power or root of the former vary? If one quantity vary as the product of two others, and if one of the latter be considered constant, how will the first vary? If one quantity vary as another, what is the former equal to? When are quantities in arithmetrical progression? When do they form an ascend. ing, and when a descending series? In an arithmetical progression, what is the last term equal to? In an ascending series, what term is the greatest, and what the least? In a descending series, what term is greatest and what the least? What is the sum of the extremes equal to ? What is the sum of all the terms equal to? In the series of odd numbers, what is the sum of the terms equal to ? If there be two ranks of quantities in arithmetical progression, how will their sum or difference be? If all the terms be multiplied or divided by the same quantity, how will their products or quotients be? When are quantities in geometrical progression? What is the last term equal to? How is the sum of the series found? When is a mathematical quantity said to be infinite? What is an infinitessimal. For all practical purposes, what are infinitessimals considered? If a finite quantity be multiplied by an infinitessimal, what will be the product? If a finite quantity be divided by an infinitessimal, what will be the quotient? How is the greatest common measure found? What is the binomial theorem? How may a residual quantity be involved? How can the roots of compound quantities be extracted? GEOMETRY. What is a point? What is a line? What are the extremities of a line? What are the intersections of one line with another? What are two straight lines? What is a superficies? What are the extremities of a superficies? What are the intersections of one superficies with another? What is a plane superficies? What is a plane rectilineal angle? What is a right angle? What an obtuse angle? What is an acute angle? What is a figure? What does area denote? What is a circle? What is the circumference of a circle? What is the diameter of a circle? What is a semi-circle? What are rectilineal figures? What are trilateral figures? What are quadrilateral figures? What are polygons? What is an equilateral triangle? What is an isosoles triangle? What is a scalene triangle? What is a right angle triangle? What is an obtuse angled triangle? What is an acute angled triangle? What is a square? What is an oblong? What is a rhombus? What is a rhomboid? What is a trapezium? What are parallel straight lines? What are the eleven axioms? What is the fourth proposition of the first book? What is the fifth and its corollary? What is the sixth and its co. rollary? What is the seventh? What is the eighth? What is the thirteenth ? What is the fourteenth? What is the fifteenth? What is the sixteenth? What is the seventeenth? What is the eighteenth ? What is the nineteenth ? What is the twentieth? What is the twenty first? What is the the twenty fourth? What is the twenty fifth? What is the twenty sixth? What is the twenty seventh? What is the twenty eighth? What is the twenty ninth? What is the thirtieth? What is the thirty second? What is the thirty third? What is the thirty fourth? What is the thirty fifth? What is the thirty sixth? What is the thirty seventh? What is the thirty eighth? What is the thirty ninth? What is the fortieth? What is the forty first? What is the forty third? What is the forty seventh? What is the forty eighth? What is every right angle par. allelogram, or rectangle said to be contained by? What is a gnomon? What is the first proposition of the second book? What is the second? What is the third? What is the fourth? [So on regular to the thirteenth, inclusive.] What is proposition A? What is proposition B? What is the radius of a circle? When does a straight line touch a circle? When do circles touch one another? When are straight lines equally distant from the center of a circle? and which is said to be farther from the center? What is an arc of a circle? What is a segment of a circle? What is an angle in a segment? and upon what does the angle insist? What is the sector of a circle? What are similar segments of a circle? What is the second proposition of the third book? [Proceed to the 16th incluclusive.] What is the eighteenth? [to the 24th, inclusive.] What is the 26th? [to the 29th, inclusive.] What is thirty first? What is the thirty second? What is the thirty fifth? What is the thirty sixth? What is the thirty seventh? When is a rectilineal figure said to be inscribed in a circle? When is a figure described about another figure? When is a rectilineal figure said to be inscribed in a circle? When is a rectilineal figure said to be described about a circle? When is a circle said to be inscribed in a rectilineal figure? When is a circle said to be described about a rectilineal figure? When is a straight line said to be placed in a circle? When is a less magnitude said to be a part of a greater? When is a greater magnitude a multiple of a less? What is ratio? When are magnitudes said to be of the same kind? When does one magnitude have the same ratio to a second that a third has to a fourth? When are mag. nitudes proportionals? When does the first have a greater ratio to the second than the third has to the fourth? and when a less? When are magnitudes continual proportionals? When is a magni. tude a mean proportional between two others? When does one magnitude have a compound ratio to another? When is the ratio of the first magnitude to the third duplicate of the ratio of the first to the second? When is the ratio of the first to the fourth triplicate of the ratio of the first to the second? What terms are homologous ? How is permutando or alternando used? How invertendo? How dividendo? How convertendo? How ex æquali (ex distantia) or ex @quo? How ex æquali? How ex æquali in proportione perturbata, seu inordinata? What are the four axioms? What is the first proposition of the fifth book? What is the second? [to the sixth inclu sive?] What is proposition A? What is B? What is C? What is the seventh? [to the 19th inclusive?] What is proposition D? What is the twentieth? [to the 24th inclusive.] What is proposition E? What is F? What are similar rectilineal figures? When are two sides of one figure reciprocally proportional to two sides of another? When is a straight line said to be cut in extreme and mean ratio? What is the altitude of any figure? What is the first proposition of the sixth book? What is the second? What is the third? What is proposition A? What is the fourth? [to the 8th inclusive.] What is the corollary to the eighth? What is the fourteenth? [to the 17th inclusive.] What is the nineteen? [to the 24th inclusive.] What is the twenty sixth? What is the twenty seventh? What is the thirty first? What is the thirty second? What is the thirty third? What are propositions B, C, D, E, F, G, H, K, severally? What is the cord of an arc of a circle? What is the perimeter of any figure? What is the area of any figure? What is the axiom in the first book of the supplement? and its corollaries? What is the first proposition of the first book of the supplement? What is the second? and its corollary? What is the third? and its two |