Finding the Circle's Center and Chords

we mean when we call figures Eegular ? Irregular ? The lines A B and B C are called chords of the Circle. How must they be placed in order to find the centre ? Describe in words how to find the centre of a Circle. What do we call the straight-line figure in the middle of the last drawing of this lesson ? Could you make a Circle round this figure to touch all the circles ? If so, where would you place the compasses ? What can you tell about the Circles in this figure ? DRAWING AND WOOD-CAEVING 15th lesson. TWENTY-FOUB SPECIMEN LESSONS 39 IN LESSON 15. If you wish to make a longer Ellipse than this, how must you place the pins ? Having drawn one chord, how do you place the other ? What do you do next in order to find the centre of the ellipse ? How many lines have you to bisect ? Having found the centre, how do you find the long axis ? Then, how do you find the short axis ? Questions on lines, angles, circles, in geometrical figure. 40 DRAWING AND WOOD-CARVING 16th lesson. Shows the comparative spaces occupied, on a piece of glass or paper, by near and distant objects. Example of the above. HOME LESSONS. Hay Work. Mallet. Square or Oblong Table. Ellipse ; find the Axes and the Foci. TWENTY-rOUE SPECIMEN LESSONS 41 IN LESSON 16. Which of the four Bottles will take up most space on your pane of glass or paper ? How can you tell the height (or level) at which your eye is, when you make this drawing of the Eailway Tunnel ? Are you standing on the same level as the men on the platform, or higher or lower ? If your eye were on the level of the platform, how would that platform be represented ? If the bar which lies between the left-hand rails were at the entrance to the Tunnel, would it appear longer or shorter than it now does ? Why does the 2nd Standard of the ' North Station ' label look shorter and narrower than the 1st ? 422 DEAWING AND WOOD-CAEVING 17th lesson. AB Draw this pattern, then make 4 inches long; divide it proportionally to the first AB, and draw pattern on that scale. HOME LESSONS. A Watch. Boole, shut, standing up, back turned. Cask or Barrel. ' TWENTY-FOUR SPECIMEN LESSONS 43 IN LESSON 17. Describe the mode of dividing the circle for the numbers on the Clock. What line of the circle is taken by the compasses for the division, and how used ? Is the roof of the Cottage above or below your eye ? Which point in this drawing is exactly opposite to your eye? What is the line called, in which that point lies ? If you went up a hill, would the horizon in your drawing be placed as it is in this drawing ? In what way would the Cottage look different if you went up a hill and looked at it from there ? What difference would there be in your view of the chim- neys ? B What kind of line is A in the last figure of Lesson 17 ? What do I mean if I say that these circles are ' similar and ' concentric ' ? 4U DEAWING AND WOOD-CARVING 18th lesson. HOME LESSONS. Sickle. Coal Scuttle. Chest of Drawers, seen end-ways, Ellipse, with circle round it, and sguare outside circle. TWENTY-FOUE SPECIMEN LESSONS 45 IN LESSON 18. If you are 5 feet taU, and you are walking with two brothers, one 6 feet tall and the other 4 feet, and each wears a straw boating-hat, how would each hat appear to you ? (Draw them.'* Which curve in this Jar will be the most round and open, the curve of the top of the jar or the dotted curve lowest down ? Tell the reason. If I put the Jar on a shelf above your head, how would the curves look then ? If you measure the first door of this Passage, and then walk along it and measure the door at the other end, which would be the largest ? Make a side representation of six lamp-posts, at equal intervals, and show on a pane of glass or paper the relative spaces which they will seem to occupy to a person looking at them through the glass. Put a circle^ and a triangle round the Geometrical Figure. What is that triangle called, and what does the name mean ? 46 DEAWING JlSD -WOOD-CABVING 19th lesson. To make any regular polygon on a given line AB. ^X HOME LESSONS. Washing-tub. Scythe. Work Box, showing right-hand end. Octagon on given line. TWENTY-FOUR SPECIMEN LESSONS 47 IN LESSON 19. What position do the top and bottom of the Hour Glass occupy to each other ? What position are the little posts in with regard to the top and bottom slabs ? Is this Box placed above or below your eye ? If it were placed on a shelf near the ceiling, what direction would the receding lines take ? What is the line on which these lines meet ? In the Polygon, to which point in the divided semicircle does the second side of the polygon always go to ? Why do we bisect the lines A B and 2 A ? What does ' bisect ' mean ? 48 DRAWING AND WOOD-CARVING 20th lesson. Within a circle make any num- ber of equal circles ; say 6. Copy these figures. Kettle. HOME LESSONS. Chisel. Broom. In a circle make 8 ec^ital circles. a circle make angles of 90�, 45�, 60� 30�- At centre of TWENTY-FOUR SPECIMEN LESSONS 49 IN LESSON 20. In fig. 1 how high is the eye of the spectator ? In fig. 2 describe how to get the six divisions in the cir- cumference of the circle. Describe how the line A B is got. Describe how to bisect the angle at B. What does this bisection give us ? Describe how figure 3 is made. In fig. 3 what is the size of the angles at the centre ? In fig. 4 how many degrees are there in the angles marked . , and in those marked o ? What is the line R line S ? P in the square called, and what the 50 DEAWING AND WOOD-UAEVING 21sT LESSON. To draw a number of equal circles round a regular polygon, touching one another and the sides of the polygon. Copy these figures 4 i>. HOME LESSONS. Pair of Compasses. Saw. Jug and Basvn. Hexagon with 6 circUi round. TWENTY-FOUB, SPECIMEN LESSONS 51 IN LESSON 21. In fig. 2 describe in words how to make the Pentagon. What is the next thing to do in carrying out this problem ? What do we obtain by that ? If you join the points 1, 2, 3, 4, 5, what figure do those lines make ? Is that figure parallel to the original pentagon ? What angles are there in figures 3, 4, 5 ? B2 DEAWING AND WOOD-CARVING 22nd lesson. Quatrefoil {4-leavea figure) HOME LESSONS. Pair of Shears. Button Hook. Vase. Make a Trefoil and a Quatrefoil from memory. TWENTY-FOUE SPECIMEN LESSONS 53 IN LESSON 22. Fig. 1. Why do you not see inside the Boat ? Why Fig. 2. do you see inside the Bell ? Fig. 3. Which angle has to be bisected in order to find the centre for the circle ? Why do we, then, make and bisect the arc 7-5 ? Fig. 6. In what position must Z S lie with regard to M 0? Which angle must we bisect ? 54 DRAWING AND WOOD-CARVING 23ED LESSON. 2 Copy these 4 figures. HOME LESSONS. Table, with Plate, Bottle, and Glass on it. Make a Heptagon (1-sided figure) in a circle. Make 5 eqtial circles in a circle. Make a Triangle voith angles of 60� and 30� ; say hovi- many degrees in the Srd angle. TWENTY-FOUE SPECIMEN LESSONS 55 IN LESSON 23. In figs. 1 and 2, is the spectator standing below or above the lamps ? � Fig. 2. What sort of angles has the front pane ? Fig. 3. How many degrees in the angles of the Triangle ? How Fig. 4. do you describe the 3 circles ? How many arcs do you make from each of the 6 points on the circumference ? How are those 6 points found ? Fig. 5. How many degrees in each angle of the Pentagon ? How many arcs are you to describe from each angle ? Fig. 6. Where do you place the compasses to make this figure ? 56 DRAWING AND WOOD-CAEVING 24th lesson. To find a circle which will pass through any 3 points ABC B .--A- HOME LESSONS. Churn,. Pickaxe. Watering- Can. Make a Hexagon, and construct 3 parallel hexagons at equal distances round the first. TWENTY-FOUB SPECIMEN LESSONS 57 IN LESSON 24. Fig. 2. How high do you stand in looking at this Pump ? Describe why we have drawn the dotted Une from the spout to the base. Is the pail touching the front of the pump, or could it go nearer? How do you find the place for the point at the top of the pump ? Figs. 3 and 4. What are the Hnes A B, B C called ? How must they be placed ? Does it matter whether they are long or short ? When rightly placed what is to be done to them ? Describe what follows when they are bisected. 58 DRAWING AND WOOD-CAEAING PATTERNS TO COPY. PATTERNS TO COPY 59 60 PKAWING AND -\VOOU-CA.KVINa ^ 61 PATTERNS TO COPY AND COMPLETE ON DIFFEBENT SCALES. Circle 3 inches in diameter. Complete it. A -B Eadins A B to be 2 inches. Complete the circle. This is i oJ pattern ; each leaf to be 2 inches long. Square of 3^ inches. Circle 3 inches in diameter. 4 squares, 2^-inch sides ; centre at C. ; ; 6S2 DEAWING AND WOOD-CAEVING A Pentagon; ABtobe Is inch. A Hexagon, with sides of 2 inches. 12 Oblongs of this pattern I inch X ^