The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |
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Page 18
... join FC , GB . A Because AF is equal to AG , and AB to AC , the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two triangles AFC , AGB ; therefore the bafe FC is e- qual to ...
... join FC , GB . A Because AF is equal to AG , and AB to AC , the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two triangles AFC , AGB ; therefore the bafe FC is e- qual to ...
Page 19
... join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the ...
... join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the ...
Page 21
... join DE , and upon it de- fcribe an equilateral triangle DEF ; then join AF ; the ftraight line AF bifects the angle BAC . Becaufe AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two fides DA , AF , are ...
... join DE , and upon it de- fcribe an equilateral triangle DEF ; then join AF ; the ftraight line AF bifects the angle BAC . Becaufe AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two fides DA , AF , are ...
Page 22
... join FC ; the ftraight line FC drawn from the given point C is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; the two AD fides DC , CF , are equal to the ...
... join FC ; the ftraight line FC drawn from the given point C is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; the two AD fides DC , CF , are equal to the ...
Page 23
... join CF , C IO . I. CH , CG ; the ftraight line CH , drawn from the given point C , is perpendicular to the given straight line AB . с I. e 8. I. Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two fides ...
... join CF , C IO . I. CH , CG ; the ftraight line CH , drawn from the given point C , is perpendicular to the given straight line AB . с I. e 8. I. Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two fides ...
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Common terms and phrases
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB ftraight line BC given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife oppofite parallel parallelepipeds parallelogram perpendicular plane angles prifms PROP propofition pyramid ratio of BC rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC wherefore
Popular passages
Page 472 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Page 170 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Page 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.
Page 167 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Page 62 - 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 of the other part.
Page 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...
Page 200 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.