corollaries? What is the fourth? and its two corollaries? What is the fifth? and its two corollaries? What is the sixth? and its two corrollaries? What is the eighth? What is the ninth? When is a straight line perpendicular to a plane? When is a plane perpendicular to a plane? What is the inclination of a straight line to a plane? What is the angle made by two planes which cut one another? When do two planes have the same inclination to one another? When is a straight line parallel to a plane? When are planes parallel to one another? What is a solid angle? What is the first proposition of the second book of the supplement? What is the second and its corollary? What is the third? [to the 21st inclusive.] What is a solid? What are similar solid figures? What is a pyramid? What is a prism? What is a parallelopiped? What What is a cube? What is a sphere? What is the axis of a sphere? What is the center of a sphere? What is the diameter of a sphere? What is a cone? What is the axis of a cone? What is the base of a cone? What is a cylinder? What is the axis of a cylinder? What are the bases of a cylinder? What are similar cones and cylinders? What is the first proposition of the third book of the supplement? What is the second? [to the 21st inclusive.] LOGARITHMS. What are logarithms? What number is taken as the base or radix ? What is done with the fractional exponents of roots and powers of roots before they are inserted in the tables? How is the logarithm of any number according to Brigg's system, obtained? Of what two parts does a logarithm generally consist? What is the integral part called? What is the index of the logarithm in respect to the number of figures in the natural number? What does the negative index show? To what is the sum of the logarithms of any two numbers equal? What--the difference of the logarithms of two numbers? What is the decimal part of the logarithm of any num. ber the same as? In a series of fractions continually decreasing, how are the indices? What do all negative logarithms belong to ? What-all positive? If a series of numbers be in geometrical progression, how will their logarithms be? How is multiplication performed by logarithms? How division? How involution? How evolution? How may a power of a root be found? How is the fourth term in proportion found? What is the arithmetical comple. ment? How is it obtained? How is compound interest calculated by logarithms? How the natural increase of population? What is an exponential equation? How is it solved? TRIGONOMETRY. Of what does trigonometry treat? Of what does plane trigonom etry treat? Of what does spherical? What is the complement of an arc or angle? What is the supplement? What is the sine of an arc? and what does it equal? What is the versed sine? What is the tangent of an arc? What is the secant? What is the co-sine of an arc? What is the co-tangent? What is the co-secant? To what are the sine of 90 degrees, the chord of 60 degrees, and the tangent of 45 degrees equal? The chord of any arc is a mean proportion. al between what? To what is the product of radius into the versed sine of the supplement of twice the given arc equal? To what is the product of the sine of the arc into the versed sine of the supple. ment of twice the arc equal? In a triangle how many parts are there? What parts must be given to enable us to find the others? For determining the parts of triangles which have not any of their sides equal to tabular radius, what proportion is used? In any right angle triangle, if the hypothenuse be made radius, what will the legs become? If either of the legs be made radius, what will the other sides become? When a side is required, what proportion is used? What--when an angle is required? To find a side what is begun with? What to find an angle? To find an angle, what must be made radius? How is the difference of the squares of two quantities obtained by logarithms? What are the three theorems for calcula. ting the sides and angles of oblique angled triangles? To find the sides and angles of an oblique angle triangle, what numbers must be given, and what may they be? When two angles and a side are given, how are the remaining sides and the other angle found? When two sides and an opposite angle are giver, how is the remaining side and the other two angles found? When two sides and the included angle are given, how is the remaining side and the other two angles found? When the three sides are given, how are the angles found? MENSURATION. How may the area of a parallelogram be found? How the area of a square? When the dimensions are given in feet and inches, how may the multiplication be performed? How is the area of a triangle found?-of a trapezoid? of a trapezium? When the trapezium can be inscribed in a circle, how may the area be found? How is the area of a regular polygon found? How is the circumference of a circle found from its diameter? How-the diameter from its circum. ference? How is the length of an arc of a circle found? How is the area of a segment of a circle found? How is the area of a circular zone found? How-the area of a lune or crescent? of a ring included between the peripheries of two concentric circles? How is the solidity of a prism found? How is the lateral surface of a right prism found? How the solidity of a pyramid ?—the lateral surface of a regular pyramid ?—the solidity of a frustum of a pyramid ?— the lateral surface of a frustum of a regular pyramid ?-the solidity of a wedge?-the solidity of a rectangular prismoid? When is a solid said to be regular? What are the regular solids? How is the surface of a regular solid found? How is the solidity of a regular solid found? How is the convex surface of a right cylinder found?— the solidity of a cylinder ?-the convex surface of a right cone ?the solidity of a frustum of a cone ?-the surface of a sphere ?—the solidity of a sphere ?-the convex surface of a segment or zone of a sphere?-the solidity of a spherical sector ?—the solidity of a spher ical segment?-the solidity of a spherical zone or frustum? What is the first proposition in isoperimetry? What is the second ?-the third?-the fourth ?-the fifth--the sixth ?-the seventh --the eighth ?--the ninth ?-the tenth ?--the eleventh ?--the twelfth ?the thirteenth ?-the fourteenth ?--the fifteenth ?--the sixteenth? HIGTHS AND DISTANCES. How is the hight of an accessible object standing on a horizontal plane, found?--of an accessible object standing on an inclined plane?--of an inaccessible object above a horizontal plane ?--of any object by observation at two stations? How is the distance of an inaccessible object found?--the distance between two objects when a passage from one to the other in a straight line is obstructed ?-the distance between two inaccessible objects?--the diameter of the earth from the known hight of a distant mountain ?--the greatest distance at which a given object can be seen on the surface of the earth ?--the distance of any heavenly body whose horizontal parallax is known? NAVIGATION. What is navigation? What is plane sailing? What is the course? What is the distance? What is the difference of latitude? What is the departure? How are distance, departure and difference of latitude measured? What are traverse tables? What is middle latitude sailing? What is the middle latitude equal to ? What is Mercator's sailing? On what are the solutions in Mercator's sailing founded? What is traverse sailing? What is resolving a traverse? If the difference of latitude, and of longitude be calculated for each part of the compound course, how may the whole difference be found? What is oblique sailing? What is current sailing? What is Hadley's quadrant? To what is its superiority owing? SURVEYING. What is the most common method of surveying a field? What are the essential parts of a surveyor's compass? What is the surveyor's chain? What is its length and number of links? What two methods are in common use for finding the contents of a piece of land? What is the rule for finding the area of a field by departure and difference of latitude? How is a field surveyed from two sta. tions? How is a field surveyed by measuring from one station? How is a field surveyed by means of the chain alone? How is an irregular boundary surveyed by means of offsets? How is the dis tance between any two points on the surface of the earth measured by means of triangles extending from one to the other? How are a given number of areas laid out in the form of a square? How is a field laid out in the form of a parallelogram, when one side and the contents are given? How is a piece of land laid out in the form of a parallelogram, the length of which shall be to the breadth in a giv. en ratio? When the area of a parallelogram is given, how may it be laid out in such a form that the length shall exceed the breadth in a given ratio? How may a triangle be laid out whose area and an. gles are given? How may the area of a triangle be divided into parts which have a given ratio to each other? How is an irregular piece of land divided into any two given parts? What is the true level? What is the apparent level? How is the difference in the hight of two places found by levelling rods? How is the difference between the true and apparent level for any given distance found? How is the difference in the hights of two places whose distance is known, found? What is the declination of the magnetic needle? and how great is it at different places? Is it uniform at the same places? How may a true meridian be drawn? CONIC SECTIONS. What is a cone? What are the three conic sections? What is the first property of the parabola? What is the second?-the third ?— the fourth--the fifth ?-the sixth ?-the seventh ?-the eighth ? What is the corollary to the eighth? What is the ninth ?--the tenth ?-the eleventh ?-the twelfth? What is property A? What is property B? What is property C? What is the first property of the ellipse? What is the second? What is the third ?--the fourth? What is the corollary to the fourth? What is the fifth property?-the sixth ?-the seventh? What is property A? What is the eighth property?-the ninth ?--the tenth? What is the corollary to the tenth? What is property B? What is the eleventh property? What is property C? What is the thirteenth property?—the four. teenth ?--the fifteenth ?-the sixteenth ?-the seventeenth? What is property D?-the eighteenth? What is property E? What is property F? What is the first property of the hyperbola ?-the second?-the third ?-the fourth ?-the fifth ?--the sixth? What is the corollary to the sixth? What is the seventh property?—the eighth? What is property A ?---the ninth ?--the tenth ?--the eleventh ?--the twelfth ?--the thirteenth ?-the fourteenth? What is property B? What is the fifteenth ? SPHERICAL TRIGONOMETRY. What is the first proposition in spherical trigonometry? What is called a great circle of a sphere? What is true of all great circles of a sphere? What is the pole of a great circle? What is a spherical angle? What is a spherical triangle? What is the second proposi tion in spherical trigonometry ?--the third, and its corollary?—the fourth, and its corollaries ?--the fifth ?-the sixth ?--the seventh ?-the eighth ?--the ninth ?-the tenth ?-the eleventh ?-the twelfth? --the thirteenth ?--the fourteenth ?-the fifteenth? What are each of the three corollaries to the fifteenth? What is the sixteenth ?-the seventeenth ?--the eighteenth ?--the nineteenth -the twenti eth? the twenty first, and its corollaries ?--the twenty second ?— the twenty third ?-the twenty fourth ?-the twenty fifth ?—the twenty sixth ?--the twenty seventh ?-the twenty eighth ?-the twenty ninth? the thirtieth, and thirty first? MECHANICS. What is mechanics? What are the essential properties of matter? What is extension ? What is impenetrability? What is gravity? How does gravity vary at different distances from the earth? How would a body remain within a hollow sphere? What is the force of gravity below the earth's surface? What is inertia? To what is the inertia of a body proportioned? How does the space described by a body moving with a uniform velocity increase? What does the space equal?-the time ?-the velocity? What is the momentum of a body? What does the momentum equal? What does the quanti. ty of matter equal? What does the velocity equal? If two bodies move with velocities which are inversely as their quantities of matter, what is true of their momenta ? What is force? What is an im. pulsive force? What is a constant force? What is the first law of motion ?-the second ?-the third? How are the spaces of bodies falling under the influence of gravity, to each other? What space would a body describe in a given time if it should move on uniformly after having acquired a given velocity, compared with the space through which it has fallen? What is the space described in any time, by a body projected downwards with a given velocity, equal to ? What is the space described by a body ascending for a given time equal to? How can the space fallen through in feet be found? How can the time of falling be found? How can the velocity be found? If two impulses communicated separately, would cause a body to describe the adjacent sides of a parallelogram, what would be their ef. fect if communicated at the same instent? What would be the combined effect of two forces, when acting separately they would describe two sides of a triangle? If a body acted upon by any number of forces would describe all the sides of a polygon except one, in a given time, what would be the effect if they all acted at the same instant? How may a given force be resolved? When the resolved forces are required to make a given angle with one another, to what will the number of pairs of forces be limited? In what condition will a body remain if acted upon by three forces represented in quantity and direction by the three sides of a triangle? By what will the proportion of three forces which keep a body at rest be represented? What is any one of the three forces which keep a body at rest? What two theorems are hence derived? What is the center of gravity? In regular plane figures, where is the center of gravity? When will two weights acting at the extremities of an inflexible rod, be in equilibrio about a given point? In any body where must the line drawn from the center of gravity fall, that the body may remain at rest? 1f a body be suspended from any point, when will it remain at rest? What is the distance of the common center of gravity of any number of bodies which have their centers of gravity in a right line, equal to? When the body or system is suspended, what is its tendency to motion the same as? What is the distance of the common |