 | John Playfair - Euclid's Elements - 1847 - 340 pages
...given angle may be divided into four equal parts, into eight, into sixteen, and so on. PROP. X. PROB. To bisect a given finite straight line, that is, to...the given straight line ; it is required to divide if into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the... | |
 | Euclides - 1847 - 128 pages
...doubling continually. A similar remark applies to the following Proposition. PROP. X. PROB. GEN. ENUN. — To bisect a given finite straight line ; that is, to divide it into two equal parts. PART. ENUN. — Let AB be the gn. st. line ; then it is required to bisect it. CONST. — Describe... | |
 | Euclides - 1848 - 52 pages
...PROP. IX. PROBLEM. To bisect a given rectilineal angle, that is, to divide it into two equal angles. PROP. X. PROBLEM. To bisect a given finite straight...line, that is, to divide it into two equal parts. PROP. XI. PROBLEM. To draw a straight line at right angles to a given straight line, from a given point... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...parts, such that the greater part may be a mean proportional between the whole line and the other part. Let AB be the given straight line; it is required to divide it into two parts at the point F, such that AB : AF:: AF:FB. At the extremity of the line AB, erect the perpendicular... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...wherefore the angles CBD, DBE, and EBA are equal to one another. 2. To trisect a given straight line. Let AB be the given straight line: It is required to divide it into three equal parts. Upon AB describe (E. i. 1.) the equilateral triangle ABC; bisect (Ei 9.) the angles... | |
 | Daniel Adams - Arithmetic - 1849 - 142 pages
...DF—CG, and draw the line CF, which will be parallel to AB. 5 PROBLEM II. To Used a given line, or to divide it into two equal parts. Let AB be the given line. With A as a center, and any radius greater than half of AB, describe arcs above and below AB,... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...edge falls on B. Then, . j*L with a pen, or pencil, draw the line AB. B PROBLEM IV. To bisect a given line : that is, to divide it into two equal parts Let AB be the given line to be divided. With A as a centre, and radius greater than half of AB, describe an arc IFE. Then,... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...same edge falls on B. Then, with a pen, or pencil, draw the line AB. B PROBLEM IV. To bisect a given line: that is, to divide it into two equal parts Let AB be the given line to be divided. With A as a centre, and radius greater than half of AB, describe an arc IF E. Then,... | |
 | Euclides - 1852 - 152 pages
...rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...rectilineal angle • BAC is bisected by the straight line AF. Which wa» to be done. PROPOSITION X. PROB. To bisect a given finite straight line, that is, to...required to divide it into two equal parts. Describe (1. i.) upon it an equilateral triangle ABC, and bisect (9. i.) the angle ACB by the straight line... | |
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To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts. 
