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That solid whose faces are six equal and regular rhombuses is called a regular rhombohedron.
269. Make in card a regular rhombohedron, show how the sides are adjusted to fit, and give a sketch of it when made.
A tangent to the complement of an arc is called the complement tangent, or the co-tangent.
270. Make a few arcs, and their tangents, and their co-tangents.
271. Make an angle, and its tangent, and also its co-tangent.
272. Can you make an angle of 130° by the line of tangents?
273. Can you find out a method of making an angle of 90° by the line of tangents?
274. Measure a few acute angles by the line of tangents.
275. Measure an obtuse angle by the line of tangents.
276. Can you make a rectangle, whose
length is 9, and breadth 4, and divide it into two parts of such a form that, being placed to touch in a certain way, they shall make a square?
277. Show that the area of a trapezium may be found by dividing the trapezium into two triangles by a diagonal, and finding the sum of the areas of such triangles.
278. Make a square, whose side shall be one-third of a foot, and show what part of a foot it contains, and how many square inches.
279. Can you, out of one piece of card, make a truncated tetrahedron, and show how you arrange the sides to fit, and give a sketch of it when made?
280. Can you make a hexagon, whose sides shall all be equal, but whose angles shall not all be equal, and that shall yet be symmetrical?
281. Can you make a right-angled trapezoid equal to a square?
282. Can you make a circle three times as large as another circle?
283. Make by the protractor a nonagon, whose sides shall be half an inch, and measure the angles of the nonagon by the line of tangents.
284. How many dodecagons may be made to touch one dodecagon at the angles?
285. How many dodecagons may be made to touch one dodecagon at the sides?
286. Show by a figure how many bricks of 9 inches by 4, laid flat, it will take to cover a square yard, and prove it by calculation.
287. Can you determine the number of bricks it would take to cover a floor, 6 yards long and 5 wide, allowing 50 for breakage?
288. How would you make a square by means of the protractor and a pencil, without pair of compasses?
289. Can you bisect an angle without using circles or arcs ?
290. Construct of one piece of card a hollow truncated cube; show on paper bow you arrange
the sides to touch, and give a sketch of the truncated cube when made.
291. Can you make a pentagon, whose side shall be one inch, without using a circle, and without having access to the centre of the pentagon?
292. Can you pass the circumference of a circle through the angular points of a triangle?
293. Show how you would find the area of a reëntrant-angled trapezium.
294. Exhibit to the eye that+1+1=1.
295. Place a circle about a quadrant. If to one extremity of an arc, not greater than that of a quadrant, there be drawn a radius, and if from the other extremity there be let fall a perpendicular to that radius, such perpendicular is called a sine of that arc.
296. Make a few arcs of circles and their sines.
297. Can you place a circle in a triangle? 298. Can you contrive to place on one line
the sines of all the degrees from 1° to 90°? in other words, can you make a line of sines?
299. Say which of the sines is equal in length to the radius of the line of sines.
300. Given the perpendicular of an equilateral triangle, to construct that equilateral triangle.
When a body has twelve equal and similar surfaces, it is called a dodecahedron.
301. Make of one piece of card a hollow dodecahedron; show on paper how you arrange the surfaces to fit, and give a sketch of the dodecahedron when made.
302. Measure by the line of sines a few acute angles.
303. Can you make an angle of 70° by the line of sines?
The sine of the complement of an arc is called the co-sine of that arc.
304. Show by a figure that the co-sine of the arc of 35° is equal to the sine of 55°.
305. Given alone the distance between the