A Second Book in Geometry

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1863 edition. Excerpt: ...If the angles are given in degrees, the simplest way is to add the two angles together, and subtract the sum from 180'; this will give the third angle, and reduce this case to the first case. But if the angles are given by being drawn, it will be better to draw the given side A B, and at one end raise the line A C, making the given adjacent angle. At any point, as C, draw C D, making A C D-i equal to the given opposite angle. Through B draw B E parallel to C D, and B E A is evidently the required triangffi Such a line as C D should be drawn lightly, so that, if necessary, it can be erased. 196. It is manifest that, in all the problems of this chapter, if the sides are given in numbers, any convenient unit may be taken to represent unity in the numbers. That is to say, if the original numbers represent feet, yards, or miles, they may in your drawing be taken as inches, tenths of inches, twentieths, or hundredths, as you please; only remembering that the same quantity must be taken as the unit in all parts of any one figure. In drawing profiles, or vertical sections, however, two units are usually employed. Thus, in drawing a sketch of the elevations and depressions of a railroad 100 miles long, in which the greatest elevation attained was 500 feet, you might represent the length on a scale of one mile to an inch, but the elevations and depressions on a scale of 400 feet or 500 feet to an inch. 197. The problem of Art. 193 is impossible if either of the given sides is greater than the sum of the other two. 198. In the second case of Art. 194, the problem is impossible if the side opposite the given angle is too short to reach the side not given. 199. In Art. 195, the problem is impossible if the sum of the angles given equals or exceeds 180....show more

Product details

• Paperback | 36 pages
• 189 x 246 x 2mm | 82g
• Miami Fl, United States
• English
• black & white illustrations
• 1236617991
• 9781236617996