Angles and Shapes in Bridges

LESSON 3. Ask questions as to the sort of lines used in Bridge. What does Tri-angle mean ? What does Equi-lateral mean ? ,, Acute , ,, Obtuse ,, ,, a Eight Angle ,, How many Eight Angles can you make at the centre of a circle ? Is an Obtuse angle larger or smaller than a Eight Angle ? Which has the greatest number of degrees, an Acute angle or an Obtuse angle ? Does a Eight angle contain more or fewer degrees than an Acute angle ? What is a Eight- angled Triangle ? How many Obtuse angles has an Obtuse-angled Triangle ? Has an Acute-angled Triangle more than one Acute -- angle ? How many ? How many Obtuse angles can you make at the centre of a circle ? (Let them try.) 16 DRAWING AND "WOOD-CAEVING 4th lesson. To bisect, or cut into two equal parts. Bisect a line. Bisect an arc, ij:. a part of a circle's circumference. / -^ I I \ I \ I >/ / /i \ Dictate a square in a circle. -- TWENTY-FOUE SPECIMEN LESSONS 17 IN LESSON 4. Ash questions about lines and angles in Ladder. What does Bi-sect mean ? Can we bisect a part of the Circumference of a circle ? --What is that part called ? How many circles are there in this pattern ? How many centres ? When two or more circles have the same centre they are called Concentric. How many angles at centre of pattern ? How many degrees in each angle ? Dictate ; thus : Make a horizontal liae 2 inches long. A Call it B. Bisect A B in 0. From make the vertical line 1 inch long above A B and 1 inch below A B, and call the ends C and D. Draw lines to join the 4 points A B C D. This figure is a square (4 sides equal and 4 angles right angles). Put your compasses at : take A as radius, and make a circle. 18 DKAWINa AJID WOOD-CAEVING 5th lesson. y Hexagon. Figure with 6 equal sides (and 6 equal angles) ; 6 equilateral tri- angles. Equilateral triangles have 3 angles of 60� each. The 3 angles of every triangle contain 180�. HOME LESSONS. Knife. Cup with handle turned to left. Bisect a line 1 inch long. TWENTY-POUK SPECIMEN LESSONS 19 IN LESSON 5. What sort of lines are those at the top of the cup, and at the top and bottom of the saucer ? Question about hnes and angles in letters. Make perpendiculars in other positions (downwards, per- pendicular to sloping lines, &c.) The 3 angles of every triangle contain 180�- How many- degrees are there in each angle of the 6 equilateral triangles ? (In this lesson and the next the month in which the lesson is given might be printed as an exercise.) 2 20 DRAWING AND WOOD-CAEVINa era LESSON. Dictate; Oblong. Pentagon. [ Figure with 5 eq^ual sides (and 5 '; equal angles). \ HOME LESSONS. Fork. Saucepan. Jam Pot. A line 'i inches long ; a line perpendicular to it at one end, and another in tlu middle. TWENTY-FOUE, SPECIMEN I^SSONS 21 IN LESSON 6. Questions on lines in Jug and Basin, and on lines and angles in Letters and Figures. How many sides has a Pentagon ? How many angles ? What angles has an oblong ? Bisect 2 sides of the Pentagon, so as to find its centre. Divide the Pentagon into 5 equal triangles. How many degrees in each of the 5 angles at the centre ? How many degrees in each of the other angles of the 5 triangles ? And how many degrees in the angles of the Pentagon ? -- -- (The date month and day might be printed as an exercise.) Give definition of an oblong. The use of the set-square might here be taught. 22 DRAWING AND WOOD-CAEVING 7th lesson. xo maKe parallel lines. TWENTY-FOUR SPECIMEN LESSONS 23 IN LESSON 7- Questions on Pail. How many lines can we make parallel to each other ? Make 6. What does ' Parallel ' mean ? How many circles in this pattern ? What are circles having the same centre called ? How many semicircles in the pattern ? What is the line 4-5 called ? Is there any other line with the same name in this pattern ?--Which ? What is the line from the centre to 5 called ? How many radii in this pattern ? 24 DBAWING AND WOOD;CAETING 8th lesson. To make an angle equal to a given angle. To divide a line into any number of equal parts. HOME LESSONS. ^ A line ^ 3 .^-n^ c!1,^s l7 ong;-S4m^scmUh.nebseBtetplvaler.eanlltWehlie nlJeiinegtsl,.ass1. inck long, av^ i z an TWENTY-FOUK SPECIMEN LESSONS 25 IN LESSON 8. Questions on Unes, angles, do., in Bowl and Kite. What do we call the part of a circle which lies between the 2 lines forming the angle A ? Describe in words how to make an angle equal to the angle at A. In the last problem on p. 24 does it signify whether we take small or large divisions on the lines A 5 and B 6 ? In what position are these 2 Unes to be to each other ? 26 DEAWING AND WOOD-CAHVING 9th lesson. To divide the line A B into parts, in the same proportion as those in CD To draw a pattern on a different scale. ^ / 2. Jl^ s- ( 2>7 HOME LESSONS. Tongs. Shovel. Tea Pot. Make a line 3| inches long ; divide it into 10 equal parts. TWENTY-FOUR SPECIMEN LESSONS 27 IN LESSON 9. If the Flower Pot (or Tub) were placed lower, would the top look more round and open, or less ? (Level of eye.) Horizontal line. Give a lesson on this. In what position must the line A B be placed with regard D to C in figs. 3 and 4 How do you find the point E ? 28 DEAWIN& AND WOOD-CAEVING 10th lesson. Show how to make a Circle with a pin and a bit of cotton. HOME LESSONS. Milk Pail. Lamp. Milk Pan. A Pentagon on line of J an inch. TWENTY-FOUE SPECIMEN LESSONS 29 IN LESSON 10. Why do we make the divisions of the Umbrella smaller as we get to the sides ? What line in the Circle is represented by the cotton ? What is the point where the pin stands ? What is the line which the pencil draws by the use of the cotton ? What is a Pentagon ? Describe in words how to make a Pentagon. Teacher draw it on the board from the pupils' dictation. 30 DRAWING AND WOOD-CAEVING llTH LESSON. Show how to make an Ellipse with 2 pins and a bit of cotton. Axis--Axes; Focus--Foci. C A.-X- To find foci: with compasses take D 5 long axis (A 0) ; from point C or Emake an arc cutting long axis in E and F and F are the foci ; the points for the pins HOME LESSONS. Axe or Satchel. Frying-pan. Hammer. Jilhpse with axes of 2i inches and 1 inch. TWENTY-FOUR SPECIMEN LESSONS 31 IN LESSON 11. Are there any straight lines in this, Kettle, and, if So, what sort are they ? What is the point E called ? and the point F ? What do we call the two points E and F ? If the EUipse is long and narrow are the Foci nearer together or farther apart than if it is short and broad ? Are there any Foci in a Circle ? Let the pupils dictate how to place the Axes and find the Foci of an Ellipse ; the Axes being given thus : the teacher drawing it on the board from the pupils' dictation. 32 DEAWING AND WOOD-CARVIISU- 12th lesson. Vanisltirig points, for lines parallel to each other, and running away from spectator on a horizontal plane. Polygon : a figure with many sides. In a circle inscribe any regular polygon. Heptagon , (7 sides).'^ HOME LESSONS. Egg in egg cup. Coal ScuttlePentagon (b-sided flgure\ in a circle. TWENTY-FOUR SPECIMEN LESSONS 33 IN LESSON 12. What shape are the glasses of the Spectacles ? (Teacher call attention to the window of the room : see how much of the outside view is seen through one pane ; i.e. a whole street, hills, woods, &c. Imagine one pane of glass your paper, on which you are to draw ; stand at the right distance for drawing on it ; transfer to a paper what you see through one pane.) Would a man (or other object) near at hand or far away look the largest ? What do we mean by a Vanishing Point ? In what line do parallel lines on a horizontal surface, or plane, vanish? What is a Polygon ? What is a Eegular Polygon ? In constructing a Regular Polygon which point of the divided diameter must the line A B always pass through ? 34 DRAWING AND WOOD-CAHVING 13th lesson. Pentagon, figure with 5 sides. Hexagon, , TWENTY-rOUE SPECIMEN LESSONS 35 IN LESSON 13. H What kind of lines are A B, C D, E F, G ? What kind of Hnes at E A, F B, G P ? -- Will E A or F B appear the longest ? Why ? What kind of angles has the box ? What kind of angles do the following appear in the draw- ing, viz.: EGP, GPA, EGH, HFE, PEG, GEA, EAB, BAP, ABF, BFB, GHF, FEA? What do we call the shape which makes the front of the box? Give the definition of that shape. Describe how to make the square in the last figure. What is a Square ? D2 36 DRAWING AND "WOOD-CAEVING 14th lesson. To find the centre of a given circle. Copy this figure. HOME LESSONS. AC A . ^'"�^ Bottle. Stool. }u>wTMike 8q,uare ; ^nscribe a circle, and show Tumbler centre of the circle. -- TWENTY-FOUE SPECIMEN LESSONS 37 IN LESSON 14. Why must the two sides in tlie Scales be exactly alike ? Say what iigures the following names describe respectively Decagon, Heptagon, Pentagon, Nonagon, Hexagon, Octagon. What do