A plain surface is one with What is a plain which a straight line may eve. surface ?-a curved ry way coincide : if not, it is surface? curved. From what do Plain figures, that are bound plain right lined ed by straight lines, take their figures take their names from the number and po names? sition of beir sides, or angles. What is the meanA Triangle is a figure having ing of the word cothree sides, and three angles, incide? fig. 7. What is the mean. { right angle triangle has one Weing of position ? of its angles right. fig. 8. 1. What is a trianOblique angled triangles have | 11 Igle? Make one. all their angles oblique. If CL TWhat is a right tbev have one obtuse angle they A B angled triangle !-an are called obtuse angled trian. oblique angled trigles, otherwise they are called angle?-an obtuse acute angled triangles, fig. 9. . angled triangle ?-an * If all the sides of a triangle be accute angled trian. equal, it is called an equilater gle? Make the seval triangle-if two sides be e. A eral kinds of trian. qual an isosceles triangle and if com gles. the three dides be all unequal. A What is an equia scalene triangle. lateral triangle ? 65. A figure of four sides is an isosceles?--a scacalled a quadrangle or quadril lene? Make them. ateral. A parallelogram is a ♡ What is the genquadrilateral which has both A erat name of four pair of its opposite sides parallel. 62 A rectangle is a parallelogram, sided figures ? What having all its angles right. is a parallelogram? A A What is a rectangle? BD C, fig 11. 1 square? rhom. A square is a figure having hoid ? a rhombus ? four equal sides and all is an What is a trape. gles right, ABD C, fig. 12. zium ? a trapezoid ? A rhomboid is an oblique an. What is a diagonal ? gle parallelogram, fig. 13 A diagonal is a A a rhombus is an equal sid. right line joining ed rhongboid, fig. 14. two opposite angles ' A trapesium is a four sided of a figure, Make a figure which has neither pair of square and then a its opposite sides parallel, fig 15. i diagonal. A trapezoid has one pair of its opposite sides parallel, fig. 16. What is the general name of figures i of more than 4 sides? Do they have 66. Figures of more than four particular names ? From what do sides are in general called poly ė they derive their particular names ? gons ; they however receive What is a pentagon ? Make one. particular names according the Whatis a hexagon ?-a heptagon ? number of their sides or angles. The term polygon is derived from A figure of five side is called a two Greek words, signifving many peniagon ; of six sides, a hexa. f corners. The particular names are gon; of seven, a heptagon; of also derived from Greek words de. eight, an octagon; of nine, a noting the number of corners in the respective figures. TOHOJDA nonagon; of len, a decagon ; of eleven, ail What is an octagon? undecagon, and of twelve a dodecagon. Iffa nonagon ?-an unpolygon have all its sides and all its apgk « cagon ?-a dodecagon? equal it is a regular polygon ; otherwise it. Lpi the pupil be rean irregular polygon. The perimeter of a fig lyenred to make each fig. ure is i be sum of all its sides. Jure on a slate or block 67. A circle is a plain figure hounded by a roard. continued curve line called the circumfer. What is a regular polence, every part of which is equally distalil gon ?-an irregular pol. from a point within called the centre, fig 17 li yon? What is the The circumference itself is sometimes calielimeter of a figuri? a circle. The periphery of a circle is the What is a circle? What same as the circumference. The radius ofil the circunsieron cm? circle is a right line drawn from the cenire to What is it soprtimes the circumference. CA, or C D, fig. 17. alled? What is the fore The diameler of a circle is a right line pass.phery of a circle? How ing through the centre and terminating iuwany degrees in the cir. the circumference. ACB lig. 17. framference of a circle ? An arc of a circle is any part of the cir (8) What is 'he radius cumference. pra circle? How many A chord is a right line joining the extreme-adii can there be to a ties of an arc. circle? Are ibey all of A segement is any part of a circle boundeuja length? What is the by an arc and its clord. diameter of a circle ?A semicircle is half a circle, or a segment How much longer than cut off by a diameter, A D B fig 17. la radius? What is an A sector is any part of a circle bounded by arc of a circle? How an arc and two radii drawn to its extremities many degrees can an auc A quadrant, or quarter of a circle is a sector have? What is a chord? having a quarter of the circumference for it. What is a eginent? What arc and its two radii perpendicular to each is the fringest chord a other A CD, or BCD, fig. 17 circle can have? Does The Height or Altitude ot a figure is a per-libe longest chord alpendicnlar let fall from an angle, or its ver-fways cut off the largest tex, to the opposite side, called the base. segment or longest arc ? The circuroference of every circle is sur-What is a semicircle ? posed to be divided into 360 equal parts, call. What is a sector? What ed Degrees: and each degree into 60 Min-is a quadrart? How uies, each minute into 60 Seconds, and so many quadrants in a se. on. Hence a semicircle contains 180 de-micircle ?-in a circle? grees, and a quadrant 90 degrees. What is the position of The Measure of an angle, is an arc of anythe radii of a quadrant ! circle contained between ihe two lines which What is the angle beform that angle, the angular point being the ween them ? Hou macentre; and it is estimated by the number of ny right angles will a degrees contained in that arc.. Thus A D is circle measure? How the measure of the angle A CD fig, 17. many degrees in a right A Secant is a line ihat cuts a circle, lying angle? What is meant partly within, and partlv without it by the altitude of a fig Twu triangles, or otber right lined figures, ure? How are all cir. are said to be mutually equilateral, when allcles supposed to be di. the sides of the one are equal to the corres-vided? How wapy de. ponding sides of the other. each to each and grees in a seinicircle they are said to be mutually equiangular, -in a quadrant? What when the angles of the one are respectively is the measure of an anequal to those of the other. Ale? How many degrees 'Identical figures, are such as are both molio a right angle? What tually equilateral and equiangular; or that is a secant? When are bave all the sides and all the angles of the liwo figures said to be e. one, respectively equal to all the sides an: Jquelaieral? What is the all the angles of the other, each to each ; suneaning of equilateral ? that if the one figure were applied to, or laid-When equiangular! upon the other, all the sides of the one would When identical? exactly fall upon and cover all the sides of the other; the two becoming as it were bui one and the same figure. Similar figures, are those that have all the ongtes of the one equal to all the angles of What are similar 6g. the other, each to each, and the sides about ures? the equal angles proportional. 68. In a right angled triangle (A B C fig.] What names are some. 8, 18,) the side (A C) opposite to the right an- times given to the three gle is called the hypothenuse ; and the other sides of a right angled two (A B and B C) the legs, or sides or base triangle and perpendicular. A Proposition, is something which is eith-| Note. There are sev. er proposed to be done, or to be demonstrat. Jeral other methods of ed, and is either a problem or a theorem. demonstrating the pre A Problem, is something proposed to beceding proposition, but done. libey cannot be well un. A Theorem, is something proposed to be derstood without con. demoustrated. siderable knowledge of A Lemma, is something which is premised, geometry, or algebra. or demonstrated, in order to render whail follows more easy. A Corollory, is a consequent truth, gaineal What is a proposition? immediately from some preceding truth or a problen? a theorean? demonstration. a lemma? a corollory A Scholium, is a remark or observation la scholium ? made upon something going before it. 69. The common Section of 2 Planes, is the line in which they meet, to cut each other. A Line is Perpendicular to a Plane, when it is perpendicular to every line in that plane which meets it. What is aplane? What One Planc is Perpendicular to Avoiber, the common section of when every line of the one, which is perpen kwo planes ? dicular to the line of their common section, When is a line per: · is perpendicolar to the other. pendicular to a plane? Parallel Planes, are such as being produced A plane perpendicular ever so far both ways, will never meet, ortio another ? which are every where at an equal perpen When are planes pardicular distance. lallel? A Solid Angle, is that which is made by What is a solid angle? three or more plane angles, meeting each other in the same point. When are solids sim. Similar Solids, contained by plane figures, ilar? are such as have all their solid angles equal, each to each, and are bounded by the same When are planes simnumber of similar planes, alike placed. lilar ? A Prism, is a solid whose ends are parallel, equal, and like plane figures, and its sides, connecting those ends, are parallelograms. | What is a prism? A Prism takes particular names accordingl to the figure of its hase, or ends, whether tri-What particular namos angular, square, rectangular, pentagonal lave prisms? hexagonal, &c. A Řight or Upright Prism, is that which ha. Wbat is the form of the planes of the sides perpendicular to the the sides of a prism? planes of the ends or base. A Parallelopiped or Parallelopipedon, is al What is a right prisno? prism bounded by six parallelograms, every opposite two of which are equal, alike, and What is a parallelopi. parallel. ped ? A Rectangular Paralleloripedon, is thall whose bounding planes are all rectangles. What is a rectangulár which are perpeadicular to each other. parallelopiped? A Cube, is a square prism, being bounded! Whja is a cube? (61) by six equal square sides or faces, which are What is a cylinder ? perpendicular to each other. A Cylinder, is a round prism, having cir-! What is the axis of a cles for its ends. cylinder? A P«rainid, is a solid, whose base is any 'What is a pyramid ? right lined plane figure, and its sides triangles, having all their verticcs meeting together is a point above the base, called (be Ver. What is a cone? tes of the pyramid. | What is the axis of a A Cone is a round pyramid having a circu-, cone? lar base ? Tth Axis of a cone, is a right line, joining! What is a solid ? t vertes, and the centre of the base. Sinilar Coves and Cylinders, are such as! When are cones and have their altitudes and the diaineters of cylinders similar? their bases proportional. A Sphere, is a solid bonnded by one curve surface, which is every wbere equally dis- What is a sphere? tant froin a certain point within, called the lat is the axis of a Centre. sphere ? The Diameter of a Sphere, is any right line passing through the centre, and termin-! What is the diameter ated both ways by the surface of a sphere? The Axis of a sphere is the same as a diameter. The Allitude of a Solid, is the perpendicu. What is the altitude lar drawn from the vertex to the opposite of a solid ? side or base. What is the vertex ? |