 ... join DB. Then AD is equal to the given straight line. And the angle ACB is equal to the sum of the angles CDB and CBD (I. 32), that is, to twice the angle CDB (I. 5). Therefore the angle ADB is half of the angle in the given segment. Hence we have...  The Mathematician - Page 3351847Full view - About this book
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...it, and the sum of the other two sides ; to construct the triangle. Let AB be the given side. Upon it describe a segment of a circle containing an angle equal to half the given angle ; and from A draw AC equal to the given sum of the two sides ; join EC-, and make the angle CBD... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...it, and the sum of the other two sides ; to construct the triangle. Let AB be the given side. Upon it describe a segment of a circle containing an angle equal to half the given angle ; and from A draw AC equal to the given sum of the two sides ; join BC ; and make the angle CBD... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...equal, each to each. This problem might also be solved by describing (III. 33.) on the given base BC a segment of a circle containing an angle equal to half the vertical angle ; by inscribing a chord BD equal to the sum of the sides ; by joining DC; and then proceeding... | |
 | John Thompson Platts, Alfred Wrigley - Mathematics - 1861 - 482 pages
...and AB is equal to BD; ie to the given difference. 131. Let АСЪе the given hypothenuse. On А С describe a segment of a circle, containing an angle equal to half a right angle, in which place the straight line AD equal to the sum of the sides. Join DC, and make... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...of the angle in the given segment. Hence we have the following synthetical solution. Describe on AB a segment of a circle containing an angle equal to half the angle in the given segment. With A as centre, and a radius equal to the given straight line, describe... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...of the angle in the given segment. Hence we have the following synthetical solution. Describe on AB a segment of a circle containing an angle equal to half the angle in the given segment. With A as centre, and a radius equal to the given straight line, describe... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 208 pages
...angle. Then as the angles OBC and OCB are equal each of them will be half a right angle. Therefore on OA describe a segment of a circle containing an angle equal to half a right angle, and take the point at which the arc of this segment cuts the given circle for the point... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...of the angle in the given segment. Hence we have the following synthetical solution. Describe on AB a segment of a circle containing an angle equal to half the angle in the given segment. With A as centre, and a radius equal to the given straight line, describe... | |
 | Patrick M. Egan - 1883 - 212 pages
...Plate XXIV. )- Take any line AB and on it describe a segment of a circle containing an angle equal to the given vertical angle ; divide AB in D in the given ratio ; from D draw DC at right angles to AB; join AC, BC; from CD cut ort' CH equal in the given perpendicular,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...of the angle in the given segment. Hence we have the following synthetical solution. Describe on AB a segment of a circle containing an angle equal to half the angle in the given segment. With A as centre, and a radius equal to the given straight line, describe... | |
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