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Oblique angled triangles have all their angles oblique. they have one obtuse angle they are called obtuse angled triangles, otherwise they are called acute angled triangles, fig. 9.

If all the sides of a triangle be equal, it is called an equilater1 al triangle-if two sides be equal an isosceles triangle and if the three dides be all unequal, a scalene triangle.

A

12

A

65. A figure of four sides is called a quadrangle or quadrilateral. A parallelogram is a quadrilateral which has both A pair of its opposite sides parallel. C A rectangle is a parallelogram, having all its angles right. A BD C, fig II.

A square is a figure having four equal sides and all is angles right, A B D C, fig. 12.

A rhomboid is an oblique an. gle parallelogram, fig. 13

A a rhombus is an equal sid ed rhomboid, fig. 14.

A trapezium is a four sided figure which has neither pair of its opposite sides parallel, fig 15.

A trapezoid has one pair of its opposite sides parallel, fig. 16. 66. Figures of more than four sides are in general called polygons; they however receive particular names according the number of their sides or angles. A figure of five side is called a peniagon; of six sides, a hexagon; of seven, a heptagon; of eight, an octagon; of nine,

a

What is a plain surface?-a curved surface ?

From what do plain right lined figures take their names?

What is the meaning of the word coincide?

What is the mean. Bing of position?

What is a triangle? Make one. What is a right

Bangled triangle ?-an oblique angled triangle?-an obtuse angled triangle ?-an

Daccute angled triangle? Make the several kinds of trian

What is an equilateral triangle ?an isosceles?--a scalene? Make them.

B

13

gles.

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16

117

D

diagonal.

What is the gen

eral name of four sided figures? What Dis a parallelogram? B What is a rectangle?

B

square?a rhomboid? a rhombus ? What is a trapezium? a trapezoid? What is a diagonal? A diagonal is a right line joining two opposite angles of a figure, Make a square and then a

What is the general name of figures of more than 4 sides? Do they have particular names? From what do they derive their particular names?

What is a pentagon? Make one. Whatis a hexagon ?-a heptagon ? The term polygon is derived from two Greek words, signifving many corners. The particular names are also derived from Greek words denoting the number of corners in the respective figures.

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What is an octagon? a nonagon?-an unecagon ?-a dodecagon? Let the pupil be re

nonagon; of ten, a decagon; of eleven, a. undecagon, and of twelve a dodecagon. If polygon have all its sides and all its angl equal it is a regular polygon; otherwise it s an irregular polygon. The perimeter of a figured to make each figure is the sum of all its sides.

ure on a slate or bisck

67. A circle is a plain figure bounded by aboard.continued curve line called the circumfer What is a regular polence. every part of which is equally dista: gon ?-an irregular polfrom a point within called the centre, fig 17 gon? What is theThe circumference itself is sometimes calle meter of a figure?— a circle. The periphery of a circle is the What is a circle? What same as the circumference. The radius of the circumierorce? circle is a right line drawn from the centre to What is it sometimes the circumference. CA, or C D, fig. 17. alled? What is the perThe diameter of a circle is a right line pass-phery of a circle? How ing through the centre and terminating iuwany degrees in the cirthe circumference. A CB fig. 17. camference of a circle? An arc of a circle is any part of the cir (8) What is the radius cumference. f a circle? How many A chord is a right line joining the extreme radii can there be to a ties of an arc. circle? Are they all of A segement is any part of a circle bounded a length? What is the by an arc and its chord. 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. Ja radius? What is an

Does

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 arc A quadrant, or quarter of a circle is a sector have? What is a chord? having a quarter of the circumference for its What is a segment? What arc and its two radii perpendicular to each is the longest chord a other A CD, or B C D, fig. 17. circle can have? The Height or Altitude of a figure is a per-be longest chord alpendicnlar let fall from an angle, or its ver-ways cut off the largest tex, to the opposite side, called the base. segment or longest arc ? The circumference of every circle is sup-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 quadrant? How utes, each minute into 60 Seconds, and so many quadrants in a seHence 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 any the radii of a quadrant? circle contained between the two lines which What is the angle beform that angle, the angular point being thetween them? How macentre; and it is estimated by the number of ny right angles will a degrees contained in that are. Thus A D is circle measure? How the measure of the angle A C D fig. 17. many degrees in a right A Secant is a line that cuts a circle, lying angle? What is meant partly within, and partly without it. by the altitude of a fig

on.

Two triangles, or other right lined figures,ure? How are all cirare said to be mutually equilateral, when all cles supposed to be dithe sides of the one are equal to the corres-vided? How many deponding sides of the other, each to each andgrees in a semicircle? 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. le? How many degrees

1dentical figures, are such as are both min a right angle? What tually equilateral and equiangular; or tha is a secant? When are bave all the sides and all the angles of the two figures said to be eone, respectively equal to all the sides and quelateral? What is the all the angles of the other, each to each; so meaning 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 bu one and the same figure.

Similar figures, are those that have all the angles of the one equal to all the angles of 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 are similar 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.

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Let A B C, figure 18, be a triangle right angle at B. On the three sides make the 3 squares A DE B, B F G C and A CHI Continue the side D A to n, IA to k, H C to m and G C till it meets A n. Thro I draw Is parallel to A B, through k draw kl parallel to A C, set the distance kl from A to o and through o draw oc parrallel to A B. Then will the square A CHI be divided into parts similar and equal to all the parts which make up the two squares A D E B and B FG C, as may be proved by measuring the parts, or by cutting them out and apply. ing them to each other. Hence the square formed on the hypothenuse or longest side of a right angled triangle is equal to the sum of the square formed on the two lege.

A Proposition, is something which is eith-f NOTE. There are sever proposed to be done, or to be demonstrat eral other methods of ed, and is either a problem or a theorem. demonstrating the preA Problem, is something proposed to be ceding proposition, but done. they cannot be well un

A Theorem, is something proposed to bederstood without condemonstrated. siderable knowledge of A Lemma, is something which is premised, geometry, or algebra. or demonstrated, in order to render what

follows more easy.

A Corollory, is a consequent truth, gained What is a proposition? immediately from some preceding truth ora problem? a theorem? demonstration. a lemma? a corollory

A Scholium, is a remark or observation a 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.

Whatis aplane? What One Plane is Perpendicular to Another, the common section of when every line of the one, which is perpen two planes? dicular to the line of their common section, When is a line per is perpendicular 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, onto another? which are every where at an equal perpendicular distance.

A Solid Angle, is that which is made by three or more plane angles, meeting each other in the same point.

When are planes par

fallel?

What is a solid angle

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 number of similar planes, alike placed.

A Prism, is a solid whose ends are parallel, equal, and like plane figures, and its sides, connecting those ends, are parallelograms.

A Prism takes particular names according to the figure of its base, or ends, whether tri angular, square, rectangular, pentagonal hexagonal, &c.

When are planes similar?

What is a prism?

What particular names have prisms?

What is the form of

A Right or Upright Prism, is that which ha the planes of the sides perpendicular to the the sides of a prism? planes of the ends or base.

A Parallelopiped or Parallelopipedon, is a prism bounded by six parallelograms, every opposite two of which are equal, alike, and parallel.

A Rectangular Parallelopipedon, is that whose bounding planes are all rectangles. which are perpendicular to each other.

What is a right prism?

What is a parallelopi

ped?

What is a rectangulăr parallelopiped?

A Cube, is a square prism, being bounded by six equal square sides or faces, which are perpendicular to each other.

A Cylinder, is a round prism, having circles for its ends.

A Pyramid, is a solid, whose base is any right lined plane figure, and its sides triangles, having all their vertices meeting togeth-| er in a point above the base, called the Vertes of the pyramid.

A Cone is a round pyramid having a circular base?

The Axis of a cone, is a right line, joining the vertex, and the centre of the base.

Similar Cones and Cylinders, are such as have their altitudes and the diameters of their bases proportional.

A Sphere, is a solid bounded by one curve surface, which is every where equally distant from a certain point within, called the

centre.

The Diameter of a Sphere, is any right line passing through the centre, and terminated both ways by the surface

The Axis of a sphere is the same as a diam

eter.

The Altitude of a Solid, is the perpendicu

Whja is a cube? (61)
What is a cylinder?

What is the axis of a cylinder?

What is a pyramid ?

What is a cone?
What is the axis of a

cone?

What is a solid ?

When are cones and cylinders similar?

What is a sphere? What is the axis of a sphere?

What is the diameter of a sphere?

What is the altitude

lar drawn from the vertex to the opposite of a solid ? side or base.

What is the vertex?

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